diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index ab58f86e0a6bcd..0105aa1c0ddcea 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -2172,7 +2172,7 @@ def _reverse_indexer(self):
         return result
 
     # reduction ops #
-    def _reduce(self, name, axis=0, skipna=True, **kwargs):
+    def _reduce(self, name, axis=0, **kwargs):
         func = getattr(self, name, None)
         if func is None:
             msg = 'Categorical cannot perform the operation {op}'
diff --git a/pandas/core/series.py b/pandas/core/series.py
index b2011fdcdee981..6ee00ecbfcf514 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -3674,8 +3674,12 @@ def _reduce(self, op, name, axis=0, skipna=True, numeric_only=None,
         if axis is not None:
             self._get_axis_number(axis)
 
-        # dispatch to ExtensionArray interface
-        if isinstance(delegate, ExtensionArray):
+        if isinstance(delegate, Categorical):
+            # TODO deprecate numeric_only argument for Categorical and use
+            # skipna as well
+            return delegate._reduce(name, numeric_only=numeric_only, **kwds)
+        elif isinstance(delegate, ExtensionArray):
+            # dispatch to ExtensionArray interface
             return delegate._reduce(name, skipna=skipna, **kwds)
         elif is_datetime64_dtype(delegate):
             # use DatetimeIndex implementation to handle skipna correctly
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index 173f719edd4655..9fca678def406f 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -960,6 +960,18 @@ def test_min_max(self):
         assert np.isnan(_min)
         assert _max == 1
 
+        cat = Series(Categorical(
+            ["a", "b", "c", "a"], categories=["b", "c", "d"], ordered=True))
+        _min = cat.min(numeric_only=True)
+        _max = cat.max(numeric_only=True)
+        assert _min == "b"
+        assert _max == "c"
+
+        _min = cat.min(numeric_only=False)
+        _max = cat.max(numeric_only=False)
+        assert np.isnan(_min)
+        assert _max == "c"
+
 
 class TestSeriesMode(object):
     # Note: the name TestSeriesMode indicates these tests