diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index 38bf57afdcb8..946692f62272 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -538,11 +538,7 @@ def update_ticks(self):
             long_axis.set_major_locator(locator)
             long_axis.set_major_formatter(formatter)
             if type(self.norm) == colors.LogNorm:
-                long_axis.set_minor_locator(_ColorbarLogLocator(self,
-                            base=10., subs='auto'))
-                long_axis.set_minor_formatter(
-                    ticker.LogFormatterSciNotation()
-                )
+                self.minorticks_on()
         else:
             _log.debug('Using fixed locator on colorbar')
             ticks, ticklabels, offset_string = self._ticker(locator, formatter)
@@ -602,6 +598,30 @@ def set_ticklabels(self, ticklabels, update_ticks=True):
             cbook._warn_external("set_ticks() must have been called.")
         self.stale = True
 
+    def minorticks_on(self):
+        """
+        Turns on the minor ticks on the colorbar without extruding
+        into the "extend regions".
+        """
+        ax = self.ax
+        long_axis = ax.yaxis if self.orientation == 'vertical' else ax.xaxis
+
+        if long_axis.get_scale() == 'log':
+            long_axis.set_minor_locator(_ColorbarLogLocator(self, base=10.,
+                                                            subs='auto'))
+            long_axis.set_minor_formatter(ticker.LogFormatterSciNotation())
+        else:
+            long_axis.set_minor_locator(_ColorbarAutoMinorLocator(self))
+
+    def minorticks_off(self):
+        """
+        Turns off the minor ticks on the colorbar.
+        """
+        ax = self.ax
+        long_axis = ax.yaxis if self.orientation == 'vertical' else ax.xaxis
+
+        long_axis.set_minor_locator(ticker.NullLocator())
+
     def _config_axes(self, X, Y):
         '''
         Make an axes patch and outline.
@@ -1209,33 +1229,6 @@ def remove(self):
             # use_gridspec was True
             ax.set_subplotspec(subplotspec)
 
-    def minorticks_on(self):
-        """
-        Turns on the minor ticks on the colorbar without extruding
-        into the "extend regions".
-        """
-        ax = self.ax
-        long_axis = ax.yaxis if self.orientation == 'vertical' else ax.xaxis
-
-        if long_axis.get_scale() == 'log':
-            cbook._warn_external('minorticks_on() has no effect on a '
-                                 'logarithmic colorbar axis')
-        else:
-            long_axis.set_minor_locator(_ColorbarAutoMinorLocator(self))
-
-    def minorticks_off(self):
-        """
-        Turns off the minor ticks on the colorbar.
-        """
-        ax = self.ax
-        long_axis = ax.yaxis if self.orientation == 'vertical' else ax.xaxis
-
-        if long_axis.get_scale() == 'log':
-            cbook._warn_external('minorticks_off() has no effect on a '
-                                 'logarithmic colorbar axis')
-        else:
-            long_axis.set_minor_locator(ticker.NullLocator())
-
 
 @docstring.Substitution(make_axes_kw_doc)
 def make_axes(parents, location=None, orientation=None, fraction=0.15,
diff --git a/lib/matplotlib/tests/test_colorbar.py b/lib/matplotlib/tests/test_colorbar.py
index 0769773252e4..fd1234221b78 100644
--- a/lib/matplotlib/tests/test_colorbar.py
+++ b/lib/matplotlib/tests/test_colorbar.py
@@ -307,6 +307,24 @@ def test_colorbar_minorticks_on_off():
         np.testing.assert_almost_equal(cbar.ax.yaxis.get_minorticklocs(),
                                        correct_minorticklocs)
 
+    # tests for github issue #13257 and PR #13265
+    data = np.random.uniform(low=1, high=10, size=(20, 20))
+
+    fig, ax = plt.subplots()
+    im = ax.pcolormesh(data, norm=LogNorm())
+    cbar = fig.colorbar(im)
+    default_minorticklocks = cbar.ax.yaxis.get_minorticklocs()
+
+    # test that minorticks turn off for LogNorm
+    cbar.minorticks_off()
+    assert np.array_equal(cbar.ax.yaxis.get_minorticklocs(),
+                          np.array([]))
+
+    # test that minorticks turn back on for LogNorm
+    cbar.minorticks_on()
+    assert np.array_equal(cbar.ax.yaxis.get_minorticklocs(),
+                          default_minorticklocks)
+
 
 def test_colorbar_autoticks():
     # Test new autotick modes. Needs to be classic because