diff --git a/doc/users/next_whats_new/colorbar_minor_ticks.rst b/doc/users/next_whats_new/colorbar_minor_ticks.rst
new file mode 100644
index 000000000000..a8b47a940875
--- /dev/null
+++ b/doc/users/next_whats_new/colorbar_minor_ticks.rst
@@ -0,0 +1,10 @@
+Add ``minorticks_on()/off()`` methods for colorbar
+--------------------------------------------------
+
+A new method :meth:`.Colobar.minorticks_on` is
+introduced to correctly display minor ticks on the colorbar. This method
+doesn't allow the minor ticks to extend into the regions beyond vmin and vmax
+when the extend `kwarg` (used while creating the colorbar) is set to 'both',
+'max' or 'min'.
+A complementary method :meth:`.Colobar.minorticks_off`
+is introduced to remove the minor ticks on the colorbar.
diff --git a/examples/color/colorbar_basics.py b/examples/color/colorbar_basics.py
index 6ba4d00477b6..adc9733f6a67 100644
--- a/examples/color/colorbar_basics.py
+++ b/examples/color/colorbar_basics.py
@@ -20,7 +20,7 @@
 Zpos = np.ma.masked_less(Z, 0)
 Zneg = np.ma.masked_greater(Z, 0)
 
-fig, (ax1, ax2) = plt.subplots(figsize=(8, 3), ncols=2)
+fig, (ax1, ax2, ax3) = plt.subplots(figsize=(13, 3), ncols=3)
 
 # plot just the positive data and save the
 # color "mappable" object returned by ax1.imshow
@@ -35,6 +35,13 @@
 neg = ax2.imshow(Zneg, cmap='Reds_r', interpolation='none')
 fig.colorbar(neg, ax=ax2)
 
+# Plot both positive and negative values betwen +/- 1.2
+pos_neg_clipped = ax3.imshow(Z, cmap='RdBu', vmin=-1.2, vmax=1.2,
+                             interpolation='none')
+# Add minorticks on the colorbar to make it easy to read the
+# values off the colorbar.
+cbar = fig.colorbar(pos_neg_clipped, ax=ax3, extend='both')
+cbar.minorticks_on()
 plt.show()
 
 #############################################################################
diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index 702d7dba955d..0670383e5b2e 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -244,6 +244,32 @@ def tick_values(self, vmin, vmax):
         return ticks[(ticks >= vmin) & (ticks <= vmax)]
 
 
+class _ColorbarAutoMinorLocator(ticker.AutoMinorLocator):
+    """
+    AutoMinorLocator for Colorbar
+
+    This locator is just a `.AutoMinorLocator` except the min and max are
+    clipped by the norm's min and max (i.e. vmin/vmax from the
+    image/pcolor/contour object).  This is necessary so that the minorticks
+    don't extrude into the "extend regions".
+    """
+
+    def __init__(self, colorbar, n=None):
+        """
+        This ticker needs to know the *colorbar* so that it can access
+        its *vmin* and *vmax*.
+        """
+        self._colorbar = colorbar
+        self.ndivs = n
+        ticker.AutoMinorLocator.__init__(self, n=None)
+
+    def __call__(self):
+        vmin = self._colorbar.norm.vmin
+        vmax = self._colorbar.norm.vmax
+        ticks = ticker.AutoMinorLocator.__call__(self)
+        return ticks[(ticks >= vmin) & (ticks <= vmax)]
+
+
 class _ColorbarLogLocator(ticker.LogLocator):
     """
     LogLocator for Colorbarbar
@@ -1164,6 +1190,33 @@ 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':
+            warnings.warn('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':
+            warnings.warn('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 d956209c599b..450d73e69697 100644
--- a/lib/matplotlib/tests/test_colorbar.py
+++ b/lib/matplotlib/tests/test_colorbar.py
@@ -270,6 +270,31 @@ def test_colorbar_ticks():
     assert len(cbar.ax.xaxis.get_ticklocs()) == len(clevs)
 
 
+def test_colorbar_minorticks_on_off():
+    # test for github issue #11510 and PR #11584
+    np.random.seed(seed=12345)
+    data = np.random.randn(20, 20)
+    with rc_context({'_internal.classic_mode': False}):
+        fig, ax = plt.subplots()
+        # purposefully setting vmin and vmax to odd fractions
+        # so as to check for the correct locations of the minor ticks
+        im = ax.pcolormesh(data, vmin=-2.3, vmax=3.3)
+
+        cbar = fig.colorbar(im, extend='both')
+        cbar.minorticks_on()
+        correct_minorticklocs = np.array([-2.2, -1.8, -1.6, -1.4, -1.2, -0.8,
+                                          -0.6, -0.4, -0.2, 0.2, 0.4, 0.6,
+                                           0.8, 1.2, 1.4, 1.6, 1.8, 2.2, 2.4,
+                                           2.6, 2.8, 3.2])
+        # testing after minorticks_on()
+        np.testing.assert_almost_equal(cbar.ax.yaxis.get_minorticklocs(),
+                                       correct_minorticklocs)
+        cbar.minorticks_off()
+        # testing after minorticks_off()
+        np.testing.assert_almost_equal(cbar.ax.yaxis.get_minorticklocs(),
+                                       np.array([]))
+
+
 def test_colorbar_autoticks():
     # Test new autotick modes. Needs to be classic because
     # non-classic doesn't go this route.