diff --git a/doc/api/next_api_changes/behavior/27179-KS.rst b/doc/api/next_api_changes/behavior/27179-KS.rst
new file mode 100644
index 000000000000..873cd622bbd4
--- /dev/null
+++ b/doc/api/next_api_changes/behavior/27179-KS.rst
@@ -0,0 +1,7 @@
+Default behavior of ``hexbin`` with *C* provided requires at least 1 point
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The behavior changed in 3.8.0 to be inclusive of *mincnt*. However that resulted in
+errors or warnings with some reduction functions, so now the default is to require at
+least 1 point to call the reduction function. This effectively restores the default
+behavior to match that of Matplotlib 3.7 and before.
diff --git a/doc/api/prev_api_changes/api_changes_3.8.0/behaviour.rst b/doc/api/prev_api_changes/api_changes_3.8.0/behaviour.rst
index 37176f99972b..fd38708c9243 100644
--- a/doc/api/prev_api_changes/api_changes_3.8.0/behaviour.rst
+++ b/doc/api/prev_api_changes/api_changes_3.8.0/behaviour.rst
@@ -165,3 +165,9 @@ PostScript paper type adds option to use figure size
 The :rc:`ps.papertype` rcParam can now be set to ``'figure'``, which will use
 a paper size that corresponds exactly with the size of the figure that is being
 saved.
+
+``hexbin`` *mincnt* parameter made consistently inclusive
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Previously, *mincnt* was inclusive with no *C* provided but exclusive when *C* is provided.
+It is now inclusive of *mincnt* in both cases.
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 9997e660f40c..b4a41099beda 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -4858,8 +4858,8 @@ def hexbin(self, x, y, C=None, gridsize=100, bins=None,
         yscale : {'linear', 'log'}, default: 'linear'
             Use a linear or log10 scale on the vertical axis.
 
-        mincnt : int > 0, default: *None*
-            If not *None*, only display cells with more than *mincnt*
+        mincnt : int >= 0, default: *None*
+            If not *None*, only display cells with at least *mincnt*
             number of points in the cell.
 
         marginals : bool, default: *False*
@@ -4926,6 +4926,11 @@ def reduce_C_function(C: array) -> float
             - `numpy.sum`: integral of the point values
             - `numpy.amax`: value taken from the largest point
 
+            By default will only reduce cells with at least 1 point because some
+            reduction functions (such as `numpy.amax`) will error/warn with empty
+            input. Changing *mincnt* will adjust the cutoff, and if set to 0 will
+            pass empty input to the reduction function.
+
         data : indexable object, optional
             DATA_PARAMETER_PLACEHOLDER
 
@@ -5023,7 +5028,7 @@ def reduce_C_function(C: array) -> float
                 else:
                     Cs_at_i2[i2[i]].append(C[i])
             if mincnt is None:
-                mincnt = 0
+                mincnt = 1
             accum = np.array(
                 [reduce_C_function(acc) if len(acc) >= mincnt else np.nan
                  for Cs_at_i in [Cs_at_i1, Cs_at_i2]
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 30992d5780ed..6c5dd712b7fd 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -965,6 +965,8 @@ def test_hexbin_empty():
     # From #23922: creating hexbin with log scaling from empty
     # dataset raises ValueError
     ax.hexbin([], [], bins='log')
+    # From #27103: np.max errors when handed empty data
+    ax.hexbin([], [], C=[], reduce_C_function=np.max)
 
 
 def test_hexbin_pickable():