diff --git a/xarray/plot/facetgrid.py b/xarray/plot/facetgrid.py
index 640bc2d5f9a..2918794b9eb 100644
--- a/xarray/plot/facetgrid.py
+++ b/xarray/plot/facetgrid.py
@@ -3,6 +3,7 @@
 import functools
 import itertools
 import warnings
+from typing import Iterable
 
 import numpy as np
 
@@ -470,39 +471,39 @@ def add_quiverkey(self, u, v, **kwargs):
         # self._adjust_fig_for_guide(self.quiverkey.text)
         return self
 
-    def set_axis_labels(self, x_var=None, y_var=None):
+    def set_axis_labels(self, *axlabels):
         """Set axis labels on the left column and bottom row of the grid."""
-        if x_var is not None:
-            if x_var in self.data.coords:
-                self._x_var = x_var
-                self.set_xlabels(label_from_attrs(self.data[x_var]))
-            else:
-                # x_var is a string
-                self.set_xlabels(x_var)
-
-        if y_var is not None:
-            if y_var in self.data.coords:
-                self._y_var = y_var
-                self.set_ylabels(label_from_attrs(self.data[y_var]))
-            else:
-                self.set_ylabels(y_var)
+        from ..core.dataarray import DataArray
+
+        for var, axis in zip(axlabels, ["x", "y", "z"]):
+            if var is not None:
+                if isinstance(var, DataArray):
+                    getattr(self, f"set_{axis}labels")(label_from_attrs(var))
+                else:
+                    getattr(self, f"set_{axis}labels")(var)
+
         return self
 
-    def set_xlabels(self, label=None, **kwargs):
-        """Label the x axis on the bottom row of the grid."""
+    def _set_labels(
+        self, axis: str, axes: Iterable, label: None | str = None, **kwargs
+    ):
         if label is None:
-            label = label_from_attrs(self.data[self._x_var])
-        for ax in self._bottom_axes:
-            ax.set_xlabel(label, **kwargs)
+            label = label_from_attrs(self.data[getattr(self, f"_{axis}_var")])
+        for ax in axes:
+            getattr(ax, f"set_{axis}label")(label, **kwargs)
         return self
 
-    def set_ylabels(self, label=None, **kwargs):
+    def set_xlabels(self, label: None | str = None, **kwargs) -> None:
+        """Label the x axis on the bottom row of the grid."""
+        self._set_labels("x", self._bottom_axes, label, **kwargs)
+
+    def set_ylabels(self, label: None | str = None, **kwargs) -> None:
         """Label the y axis on the left column of the grid."""
-        if label is None:
-            label = label_from_attrs(self.data[self._y_var])
-        for ax in self._left_axes:
-            ax.set_ylabel(label, **kwargs)
-        return self
+        self._set_labels("y", self._left_axes, label, **kwargs)
+
+    def set_zlabels(self, label: None | str = None, **kwargs) -> None:
+        """Label the z axis."""
+        self._set_labels("z", self._left_axes, label, **kwargs)
 
     def set_titles(self, template="{coord} = {value}", maxchar=30, size=None, **kwargs):
         """