diff --git a/NEWS.md b/NEWS.md
index 851575c3d0702..182b655474f2c 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -26,6 +26,7 @@ Standard library changes
 ------------------------
 
   * `CartesianIndices` can now be constructed from two `CartesianIndex`es `I` and `J` with `I:J` ([#29440]).
+  * `CartesianIndices` support broadcasting arithmetic (+ and -) with a `CartesianIndex` ([#29890]).
   * `copy!` support for arrays, dicts, and sets has been moved to Base from the Future package ([#29173]).
   * Channels now convert inserted values (like containers) instead of requiring types to match ([#29092]).
   * `range` can accept the stop value as a positional argument, e.g. `range(1,10,step=2)` ([#28708]).
diff --git a/base/broadcast.jl b/base/broadcast.jl
index 0eb2362b8a497..e55678bb5e0cc 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -1006,6 +1006,18 @@ broadcasted(::DefaultArrayStyle{1}, ::typeof(big), r::StepRange) = big(r.start):
 broadcasted(::DefaultArrayStyle{1}, ::typeof(big), r::StepRangeLen) = StepRangeLen(big(r.ref), big(r.step), length(r), r.offset)
 broadcasted(::DefaultArrayStyle{1}, ::typeof(big), r::LinRange) = LinRange(big(r.start), big(r.stop), length(r))
 
+## CartesianIndices
+broadcasted(::typeof(+), I::CartesianIndices{N}, j::CartesianIndex{N}) where N =
+    CartesianIndices(map((rng, offset)->rng .+ offset, I.indices, Tuple(j)))
+broadcasted(::typeof(+), j::CartesianIndex{N}, I::CartesianIndices{N}) where N =
+    I .+ j
+broadcasted(::typeof(-), I::CartesianIndices{N}, j::CartesianIndex{N}) where N =
+    CartesianIndices(map((rng, offset)->rng .- offset, I.indices, Tuple(j)))
+function broadcasted(::typeof(-), j::CartesianIndex{N}, I::CartesianIndices{N}) where N
+    diffrange(offset, rng) = range(offset-last(rng), length=length(rng))
+    Iterators.reverse(CartesianIndices(map(diffrange, Tuple(j), I.indices)))
+end
+
 ## In specific instances, we can broadcast masked BitArrays whole chunks at a time
 # Very intentionally do not support much functionality here: scalar indexing would be O(n)
 struct BitMaskedBitArray{N,M}
diff --git a/test/abstractarray.jl b/test/abstractarray.jl
index 6c5027a673847..d53916a05f31a 100644
--- a/test/abstractarray.jl
+++ b/test/abstractarray.jl
@@ -909,6 +909,11 @@ end
         J1, J2 = @inferred(promote(I1, I2))
         @test J1 === J2
     end
+
+    i = CartesianIndex(17,-2)
+    @test CR .+ i === i .+ CR === CartesianIndices((19:21, -1:3))
+    @test CR .- i === CartesianIndices((-15:-13, 3:7))
+    @test collect(i .- CR) == Ref(i) .- collect(CR)
 end
 
 @testset "issue #25770" begin