diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 6d28fae6c2d9..0ce2f52acf54 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1530,14 +1530,31 @@ def set_units(self, u):
         Parameters
         ----------
         u : units tag
+
+        Notes
+        -----
+        The units of any shared axis will also be updated.
         """
         if u == self.units:
             return
-        self.units = u
-        self._update_axisinfo()
-        self.callbacks.process('units')
-        self.callbacks.process('units finalize')
-        self.stale = True
+        if self is self.axes.xaxis:
+            shared = [
+                ax.xaxis
+                for ax in self.axes.get_shared_x_axes().get_siblings(self.axes)
+            ]
+        elif self is self.axes.yaxis:
+            shared = [
+                ax.yaxis
+                for ax in self.axes.get_shared_y_axes().get_siblings(self.axes)
+            ]
+        else:
+            shared = [self]
+        for axis in shared:
+            axis.units = u
+            axis._update_axisinfo()
+            axis.callbacks.process('units')
+            axis.callbacks.process('units finalize')
+            axis.stale = True
 
     def get_units(self):
         """Return the units for axis."""
diff --git a/lib/matplotlib/tests/test_units.py b/lib/matplotlib/tests/test_units.py
index 252136b4dfb4..3f40a99a2f5a 100644
--- a/lib/matplotlib/tests/test_units.py
+++ b/lib/matplotlib/tests/test_units.py
@@ -1,10 +1,11 @@
-from datetime import datetime
+from datetime import datetime, timezone, timedelta
 import platform
 from unittest.mock import MagicMock
 
 import matplotlib.pyplot as plt
 from matplotlib.testing.decorators import check_figures_equal, image_comparison
 import matplotlib.units as munits
+from matplotlib.category import UnitData
 import numpy as np
 import pytest
 
@@ -127,12 +128,12 @@ def test_jpl_bar_units():
     units.register()
 
     day = units.Duration("ET", 24.0 * 60.0 * 60.0)
-    x = [0*units.km, 1*units.km, 2*units.km]
-    w = [1*day, 2*day, 3*day]
+    x = [0 * units.km, 1 * units.km, 2 * units.km]
+    w = [1 * day, 2 * day, 3 * day]
     b = units.Epoch("ET", dt=datetime(2009, 4, 25))
     fig, ax = plt.subplots()
     ax.bar(x, w, bottom=b)
-    ax.set_ylim([b-1*day, b+w[-1]+(1.001)*day])
+    ax.set_ylim([b - 1 * day, b + w[-1] + (1.001) * day])
 
 
 @image_comparison(['jpl_barh_units.png'],
@@ -142,13 +143,13 @@ def test_jpl_barh_units():
     units.register()
 
     day = units.Duration("ET", 24.0 * 60.0 * 60.0)
-    x = [0*units.km, 1*units.km, 2*units.km]
-    w = [1*day, 2*day, 3*day]
+    x = [0 * units.km, 1 * units.km, 2 * units.km]
+    w = [1 * day, 2 * day, 3 * day]
     b = units.Epoch("ET", dt=datetime(2009, 4, 25))
 
     fig, ax = plt.subplots()
     ax.barh(x, w, left=b)
-    ax.set_xlim([b-1*day, b+w[-1]+(1.001)*day])
+    ax.set_xlim([b - 1 * day, b + w[-1] + (1.001) * day])
 
 
 def test_empty_arrays():
@@ -172,3 +173,41 @@ class subdate(datetime):
 
     fig_test.subplots().plot(subdate(2000, 1, 1), 0, "o")
     fig_ref.subplots().plot(datetime(2000, 1, 1), 0, "o")
+
+
+def test_shared_axis_quantity(quantity_converter):
+    munits.registry[Quantity] = quantity_converter
+    x = Quantity(np.linspace(0, 1, 10), "hours")
+    y1 = Quantity(np.linspace(1, 2, 10), "feet")
+    y2 = Quantity(np.linspace(3, 4, 10), "feet")
+    fig, (ax1, ax2) = plt.subplots(2, 1, sharex='all', sharey='all')
+    ax1.plot(x, y1)
+    ax2.plot(x, y2)
+    assert ax1.xaxis.get_units() == ax2.xaxis.get_units() == "hours"
+    assert ax2.yaxis.get_units() == ax2.yaxis.get_units() == "feet"
+    ax1.xaxis.set_units("seconds")
+    ax2.yaxis.set_units("inches")
+    assert ax1.xaxis.get_units() == ax2.xaxis.get_units() == "seconds"
+    assert ax1.yaxis.get_units() == ax2.yaxis.get_units() == "inches"
+
+
+def test_shared_axis_datetime():
+    # datetime uses dates.DateConverter
+    y1 = [datetime(2020, i, 1, tzinfo=timezone.utc) for i in range(1, 13)]
+    y2 = [datetime(2021, i, 1, tzinfo=timezone.utc) for i in range(1, 13)]
+    fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True)
+    ax1.plot(y1)
+    ax2.plot(y2)
+    ax1.yaxis.set_units(timezone(timedelta(hours=5)))
+    assert ax2.yaxis.units == timezone(timedelta(hours=5))
+
+
+def test_shared_axis_categorical():
+    # str uses category.StrCategoryConverter
+    d1 = {"a": 1, "b": 2}
+    d2 = {"a": 3, "b": 4}
+    fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, sharey=True)
+    ax1.plot(d1.keys(), d1.values())
+    ax2.plot(d2.keys(), d2.values())
+    ax1.xaxis.set_units(UnitData(["c", "d"]))
+    assert "c" in ax2.xaxis.get_units()._mapping.keys()