diff --git a/NEWS.md b/NEWS.md
index 4c9fb2f09c..ab4b2080fd 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,8 @@
 # ggplot2 (development version)
 
+* Discrete scales now support `minor_breaks`. This may only make sense in
+  discrete position scales, where it affects the placement of minor ticks
+  and minor gridlines (#5434).
 * Discrete position scales now expose the `palette` argument, which can be used 
   to customise spacings between levels (@teunbrand, #5770).
 * The default `se` parameter in layers with `geom = "smooth"` will be `TRUE` 
diff --git a/R/guide-axis.R b/R/guide-axis.R
index 8eafccf114..dc57ffd23e 100644
--- a/R/guide-axis.R
+++ b/R/guide-axis.R
@@ -136,6 +136,11 @@ GuideAxis <- ggproto(
 
     if (nrow(major) > 0) {
       major$.type <- "major"
+      if (!vec_is(minor$.value, major$.value)) {
+        # If we have mixed types of values, which may happen in discrete scales,
+        # discard minor values in favour of the major values.
+        minor$.value <- NULL
+      }
       vec_rbind(major, minor)
     } else {
       minor
diff --git a/R/scale-.R b/R/scale-.R
index 6233caf54f..9eaa153590 100644
--- a/R/scale-.R
+++ b/R/scale-.R
@@ -23,13 +23,13 @@
 #'     Also accepts rlang [lambda][rlang::as_function()] function notation.
 #' @param minor_breaks One of:
 #'   - `NULL` for no minor breaks
-#'   - `waiver()` for the default breaks (one minor break between
-#'     each major break)
+#'   - `waiver()` for the default breaks (none for discrete, one minor break
+#'     between each major break for continuous)
 #'   - A numeric vector of positions
 #'   - A function that given the limits returns a vector of minor breaks. Also
 #'     accepts rlang [lambda][rlang::as_function()] function notation. When
 #'     the function has two arguments, it will be given the limits and major
-#'     breaks.
+#'     break positions.
 #' @param n.breaks An integer guiding the number of major breaks. The algorithm
 #'   may choose a slightly different number to ensure nice break labels. Will
 #'   only have an effect if `breaks = waiver()`. Use `NULL` to use the default
@@ -200,7 +200,8 @@ continuous_scale <- function(aesthetics, scale_name = deprecated(), palette, nam
 #' The `r link_book("new scales section", "extensions#sec-new-scales")`
 #' @keywords internal
 discrete_scale <- function(aesthetics, scale_name = deprecated(), palette, name = waiver(),
-                           breaks = waiver(), labels = waiver(), limits = NULL, expand = waiver(),
+                           breaks = waiver(), minor_breaks = waiver(),
+                           labels = waiver(), limits = NULL, expand = waiver(),
                            na.translate = TRUE, na.value = NA, drop = TRUE,
                            guide = "legend", position = "left",
                            call = caller_call(),
@@ -218,6 +219,7 @@ discrete_scale <- function(aesthetics, scale_name = deprecated(), palette, name
   limits <- allow_lambda(limits)
   breaks <- allow_lambda(breaks)
   labels <- allow_lambda(labels)
+  minor_breaks <- allow_lambda(minor_breaks)
 
   if (!is.function(limits) && (length(limits) > 0) && !is.discrete(limits)) {
     cli::cli_warn(c(
@@ -247,6 +249,7 @@ discrete_scale <- function(aesthetics, scale_name = deprecated(), palette, name
 
     name = name,
     breaks = breaks,
+    minor_breaks = minor_breaks,
     labels = labels,
     drop = drop,
     guide = guide,
@@ -1022,7 +1025,34 @@ ScaleDiscrete <- ggproto("ScaleDiscrete", Scale,
     structure(in_domain, pos = match(in_domain, breaks))
   },
 
-  get_breaks_minor = function(...) NULL,
+  get_breaks_minor = function(self, n = 2, b = self$break_positions(),
+                              limits = self$get_limits()) {
+    breaks <- self$minor_breaks
+    # The default is to draw no minor ticks
+    if (is.null(breaks %|W|% NULL)) {
+      return(NULL)
+    }
+    if (is.function(breaks)) {
+      # Ensure function gets supplied numeric limits and breaks
+      if (!is.numeric(b)) {
+        b <- self$map(b)
+      }
+      if (!is.numeric(limits)) {
+        limits <- self$map(limits)
+        limits <- self$dimension(self$expand, limits)
+      }
+
+      # Allow for two types of minor breaks specifications
+      break_fun <- fetch_ggproto(self, "minor_breaks")
+      arg_names <- fn_fmls_names(break_fun)
+      if (length(arg_names) == 1L) {
+        breaks <- break_fun(limits)
+      } else {
+        breaks <- break_fun(limits, b)
+      }
+    }
+    breaks
+  },
 
   get_labels = function(self, breaks = self$get_breaks()) {
     if (self$is_empty()) {
diff --git a/R/scale-view.R b/R/scale-view.R
index 3a068ea81c..de78ebffb6 100644
--- a/R/scale-view.R
+++ b/R/scale-view.R
@@ -15,17 +15,16 @@
 view_scale_primary <- function(scale, limits = scale$get_limits(),
                                continuous_range = scale$dimension(limits = limits)) {
 
+  # continuous_range can be specified in arbitrary order, but
+  # scales expect the one in ascending order.
+  continuous_scale_sorted <- sort(continuous_range)
   if(!scale$is_discrete()) {
-    # continuous_range can be specified in arbitrary order, but
-    # continuous scales expect the one in ascending order.
-    continuous_scale_sorted <- sort(continuous_range)
     breaks <- scale$get_breaks(continuous_scale_sorted)
-    minor_breaks <- scale$get_breaks_minor(b = breaks, limits = continuous_scale_sorted)
     breaks <- censor(breaks, continuous_scale_sorted, only.finite = FALSE)
   } else {
     breaks <- scale$get_breaks(limits)
-    minor_breaks <- scale$get_breaks_minor(b = breaks, limits = limits)
   }
+  minor_breaks <- scale$get_breaks_minor(b = breaks, limits = continuous_scale_sorted)
   minor_breaks <- censor(minor_breaks, continuous_range, only.finite = FALSE)
 
   ggproto(NULL, ViewScale,
diff --git a/man/continuous_scale.Rd b/man/continuous_scale.Rd
index dc4abffbce..a572ec2bf7 100644
--- a/man/continuous_scale.Rd
+++ b/man/continuous_scale.Rd
@@ -56,13 +56,13 @@ Also accepts rlang \link[rlang:as_function]{lambda} function notation.
 \item{minor_breaks}{One of:
 \itemize{
 \item \code{NULL} for no minor breaks
-\item \code{waiver()} for the default breaks (one minor break between
-each major break)
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
 \item A numeric vector of positions
 \item A function that given the limits returns a vector of minor breaks. Also
 accepts rlang \link[rlang:as_function]{lambda} function notation. When
 the function has two arguments, it will be given the limits and major
-breaks.
+break positions.
 }}
 
 \item{n.breaks}{An integer guiding the number of major breaks. The algorithm
diff --git a/man/discrete_scale.Rd b/man/discrete_scale.Rd
index 0fd213cd30..ae349cdf1f 100644
--- a/man/discrete_scale.Rd
+++ b/man/discrete_scale.Rd
@@ -10,6 +10,7 @@ discrete_scale(
   palette,
   name = waiver(),
   breaks = waiver(),
+  minor_breaks = waiver(),
   labels = waiver(),
   limits = NULL,
   expand = waiver(),
@@ -47,6 +48,18 @@ as output. Also accepts rlang \link[rlang:as_function]{lambda} function
 notation.
 }}
 
+\item{minor_breaks}{One of:
+\itemize{
+\item \code{NULL} for no minor breaks
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
+\item A numeric vector of positions
+\item A function that given the limits returns a vector of minor breaks. Also
+accepts rlang \link[rlang:as_function]{lambda} function notation. When
+the function has two arguments, it will be given the limits and major
+break positions.
+}}
+
 \item{labels}{One of:
 \itemize{
 \item \code{NULL} for no labels
diff --git a/man/scale_continuous.Rd b/man/scale_continuous.Rd
index 56c23639a6..153bb325f5 100644
--- a/man/scale_continuous.Rd
+++ b/man/scale_continuous.Rd
@@ -78,13 +78,13 @@ Also accepts rlang \link[rlang:as_function]{lambda} function notation.
 \item{minor_breaks}{One of:
 \itemize{
 \item \code{NULL} for no minor breaks
-\item \code{waiver()} for the default breaks (one minor break between
-each major break)
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
 \item A numeric vector of positions
 \item A function that given the limits returns a vector of minor breaks. Also
 accepts rlang \link[rlang:as_function]{lambda} function notation. When
 the function has two arguments, it will be given the limits and major
-breaks.
+break positions.
 }}
 
 \item{n.breaks}{An integer guiding the number of major breaks. The algorithm
diff --git a/man/scale_discrete.Rd b/man/scale_discrete.Rd
index 381c09254e..0bab3ad985 100644
--- a/man/scale_discrete.Rd
+++ b/man/scale_discrete.Rd
@@ -63,6 +63,17 @@ from a discrete scale, specify \code{na.translate = FALSE}.}
 missing values be displayed as? Does not apply to position scales
 where \code{NA} is always placed at the far right.}
     \item{\code{aesthetics}}{The names of the aesthetics that this scale works with.}
+    \item{\code{minor_breaks}}{One of:
+\itemize{
+\item \code{NULL} for no minor breaks
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
+\item A numeric vector of positions
+\item A function that given the limits returns a vector of minor breaks. Also
+accepts rlang \link[rlang:as_function]{lambda} function notation. When
+the function has two arguments, it will be given the limits and major
+break positions.
+}}
     \item{\code{labels}}{One of:
 \itemize{
 \item \code{NULL} for no labels
diff --git a/man/scale_gradient.Rd b/man/scale_gradient.Rd
index cbc5427282..368ef16509 100644
--- a/man/scale_gradient.Rd
+++ b/man/scale_gradient.Rd
@@ -120,13 +120,13 @@ Also accepts rlang \link[rlang:as_function]{lambda} function notation.
     \item{\code{minor_breaks}}{One of:
 \itemize{
 \item \code{NULL} for no minor breaks
-\item \code{waiver()} for the default breaks (one minor break between
-each major break)
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
 \item A numeric vector of positions
 \item A function that given the limits returns a vector of minor breaks. Also
 accepts rlang \link[rlang:as_function]{lambda} function notation. When
 the function has two arguments, it will be given the limits and major
-breaks.
+break positions.
 }}
     \item{\code{n.breaks}}{An integer guiding the number of major breaks. The algorithm
 may choose a slightly different number to ensure nice break labels. Will
diff --git a/man/scale_grey.Rd b/man/scale_grey.Rd
index e085fa0016..6b04f40688 100644
--- a/man/scale_grey.Rd
+++ b/man/scale_grey.Rd
@@ -61,6 +61,17 @@ every level in a legend, the layer should use \code{show.legend = TRUE}.}
     \item{\code{na.translate}}{Unlike continuous scales, discrete scales can easily show
 missing values, and do so by default. If you want to remove missing values
 from a discrete scale, specify \code{na.translate = FALSE}.}
+    \item{\code{minor_breaks}}{One of:
+\itemize{
+\item \code{NULL} for no minor breaks
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
+\item A numeric vector of positions
+\item A function that given the limits returns a vector of minor breaks. Also
+accepts rlang \link[rlang:as_function]{lambda} function notation. When
+the function has two arguments, it will be given the limits and major
+break positions.
+}}
     \item{\code{labels}}{One of:
 \itemize{
 \item \code{NULL} for no labels
diff --git a/man/scale_hue.Rd b/man/scale_hue.Rd
index 0ec49fd123..99776d95d3 100644
--- a/man/scale_hue.Rd
+++ b/man/scale_hue.Rd
@@ -67,6 +67,17 @@ every level in a legend, the layer should use \code{show.legend = TRUE}.}
     \item{\code{na.translate}}{Unlike continuous scales, discrete scales can easily show
 missing values, and do so by default. If you want to remove missing values
 from a discrete scale, specify \code{na.translate = FALSE}.}
+    \item{\code{minor_breaks}}{One of:
+\itemize{
+\item \code{NULL} for no minor breaks
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
+\item A numeric vector of positions
+\item A function that given the limits returns a vector of minor breaks. Also
+accepts rlang \link[rlang:as_function]{lambda} function notation. When
+the function has two arguments, it will be given the limits and major
+break positions.
+}}
     \item{\code{labels}}{One of:
 \itemize{
 \item \code{NULL} for no labels
diff --git a/man/scale_linetype.Rd b/man/scale_linetype.Rd
index 94eeb93927..da4cf2b7c3 100644
--- a/man/scale_linetype.Rd
+++ b/man/scale_linetype.Rd
@@ -53,6 +53,17 @@ every level in a legend, the layer should use \code{show.legend = TRUE}.}
 missing values, and do so by default. If you want to remove missing values
 from a discrete scale, specify \code{na.translate = FALSE}.}
     \item{\code{aesthetics}}{The names of the aesthetics that this scale works with.}
+    \item{\code{minor_breaks}}{One of:
+\itemize{
+\item \code{NULL} for no minor breaks
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
+\item A numeric vector of positions
+\item A function that given the limits returns a vector of minor breaks. Also
+accepts rlang \link[rlang:as_function]{lambda} function notation. When
+the function has two arguments, it will be given the limits and major
+break positions.
+}}
     \item{\code{labels}}{One of:
 \itemize{
 \item \code{NULL} for no labels
diff --git a/man/scale_manual.Rd b/man/scale_manual.Rd
index 9857dcbc65..92205f3013 100644
--- a/man/scale_manual.Rd
+++ b/man/scale_manual.Rd
@@ -64,6 +64,17 @@ from a discrete scale, specify \code{na.translate = FALSE}.}
 \code{waiver()}, the default, the name of the scale is taken from the first
 mapping used for that aesthetic. If \code{NULL}, the legend title will be
 omitted.}
+    \item{\code{minor_breaks}}{One of:
+\itemize{
+\item \code{NULL} for no minor breaks
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
+\item A numeric vector of positions
+\item A function that given the limits returns a vector of minor breaks. Also
+accepts rlang \link[rlang:as_function]{lambda} function notation. When
+the function has two arguments, it will be given the limits and major
+break positions.
+}}
     \item{\code{labels}}{One of:
 \itemize{
 \item \code{NULL} for no labels
diff --git a/man/scale_shape.Rd b/man/scale_shape.Rd
index 65deec3ea2..ffbb381481 100644
--- a/man/scale_shape.Rd
+++ b/man/scale_shape.Rd
@@ -53,6 +53,17 @@ from a discrete scale, specify \code{na.translate = FALSE}.}
 missing values be displayed as? Does not apply to position scales
 where \code{NA} is always placed at the far right.}
     \item{\code{aesthetics}}{The names of the aesthetics that this scale works with.}
+    \item{\code{minor_breaks}}{One of:
+\itemize{
+\item \code{NULL} for no minor breaks
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
+\item A numeric vector of positions
+\item A function that given the limits returns a vector of minor breaks. Also
+accepts rlang \link[rlang:as_function]{lambda} function notation. When
+the function has two arguments, it will be given the limits and major
+break positions.
+}}
     \item{\code{labels}}{One of:
 \itemize{
 \item \code{NULL} for no labels
diff --git a/man/scale_size.Rd b/man/scale_size.Rd
index c1c7d8dd05..753ecfa790 100644
--- a/man/scale_size.Rd
+++ b/man/scale_size.Rd
@@ -134,13 +134,13 @@ breaks are given explicitly.}
     \item{\code{minor_breaks}}{One of:
 \itemize{
 \item \code{NULL} for no minor breaks
-\item \code{waiver()} for the default breaks (one minor break between
-each major break)
+\item \code{waiver()} for the default breaks (none for discrete, one minor break
+between each major break for continuous)
 \item A numeric vector of positions
 \item A function that given the limits returns a vector of minor breaks. Also
 accepts rlang \link[rlang:as_function]{lambda} function notation. When
 the function has two arguments, it will be given the limits and major
-breaks.
+break positions.
 }}
     \item{\code{oob}}{One of:
 \itemize{
diff --git a/tests/testthat/_snaps/prohibited-functions.md b/tests/testthat/_snaps/prohibited-functions.md
index 87c26e26a8..f2aa9bf4d2 100644
--- a/tests/testthat/_snaps/prohibited-functions.md
+++ b/tests/testthat/_snaps/prohibited-functions.md
@@ -29,7 +29,7 @@
       [4] "date_minor_breaks"
       
       $discrete_scale
-      [1] "scale_name"
+      [1] "scale_name"   "minor_breaks"
       
       $geom_density2d
       [1] "contour_var"