diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index d4a8521eb3cbff..d9e77e9a362f83 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -2179,7 +2179,7 @@ def _reduce(self, name, axis=0, **kwargs):
             raise TypeError(msg.format(op=name))
         return func(**kwargs)
 
-    def min(self, skipna=None, **kwargs):
+    def min(self, skipna=True, **kwargs):
         """
         The minimum value of the object.
 
@@ -2205,7 +2205,7 @@ def min(self, skipna=None, **kwargs):
         else:
             return self.categories[pointer]
 
-    def max(self, skipna=None, **kwargs):
+    def max(self, skipna=True, **kwargs):
         """
         The maximum value of the object.
 
diff --git a/pandas/tests/arrays/categorical/test_analytics.py b/pandas/tests/arrays/categorical/test_analytics.py
index 5efcd527de8d82..fc8bfda9f3b4e5 100644
--- a/pandas/tests/arrays/categorical/test_analytics.py
+++ b/pandas/tests/arrays/categorical/test_analytics.py
@@ -36,26 +36,26 @@ def test_min_max(self):
 
         cat = Categorical([np.nan, "b", "c", np.nan],
                           categories=['d', 'c', 'b', 'a'], ordered=True)
-        _min = cat.min()
-        _max = cat.max()
+        _min = cat.min(skipna=False)
+        _max = cat.max(skipna=False)
         assert np.isnan(_min)
         assert _max == "b"
 
-        _min = cat.min(numeric_only=True)
+        _min = cat.min()
         assert _min == "c"
-        _max = cat.max(numeric_only=True)
+        _max = cat.max()
         assert _max == "b"
 
         cat = Categorical([np.nan, 1, 2, np.nan], categories=[5, 4, 3, 2, 1],
                           ordered=True)
-        _min = cat.min()
-        _max = cat.max()
+        _min = cat.min(skipna=False)
+        _max = cat.max(skipna=False)
         assert np.isnan(_min)
         assert _max == 1
 
-        _min = cat.min(numeric_only=True)
+        _min = cat.min()
         assert _min == 2
-        _max = cat.max(numeric_only=True)
+        _max = cat.max()
         assert _max == 1
 
     @pytest.mark.parametrize("values,categories,exp_mode", [
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index 173f719edd4655..0df880a41fe59e 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -948,8 +948,8 @@ def test_min_max(self):
         cat = Series(Categorical(
             [np.nan, "b", "c", np.nan], categories=['d', 'c', 'b', 'a'
                                                     ], ordered=True))
-        _min = cat.min()
-        _max = cat.max()
+        _min = cat.min(skipna=False)
+        _max = cat.max(skipna=False)
         assert np.isnan(_min)
         assert _max == "b"
 
@@ -957,9 +957,16 @@ def test_min_max(self):
             [np.nan, 1, 2, np.nan], categories=[5, 4, 3, 2, 1], ordered=True))
         _min = cat.min()
         _max = cat.max()
-        assert np.isnan(_min)
+        assert _min == 2
         assert _max == 1
 
+        cat = Series(Categorical(
+            ["a", "b", "c", "a"], categories=["b", "c", "d"], ordered=True))
+        _min = cat.min()
+        _max = cat.max()
+        assert _min == "b"
+        assert _max == "c"
+
 
 class TestSeriesMode(object):
     # Note: the name TestSeriesMode indicates these tests
diff --git a/pandas/tests/series/test_analytics.py b/pandas/tests/series/test_analytics.py
index c8b9dcfee956a1..6811e370726b29 100644
--- a/pandas/tests/series/test_analytics.py
+++ b/pandas/tests/series/test_analytics.py
@@ -1497,11 +1497,3 @@ def test_drop_duplicates_categorical_bool(self, is_ordered):
         sc = tc.copy()
         sc.drop_duplicates(keep=False, inplace=True)
         tm.assert_series_equal(sc, tc[~expected])
-
-    def test_min_skipna(self):
-        raw_cat = pd.Categorical(["a", "b", "c", "a"],
-                                 categories=["b", "c", "d"],
-                                 ordered=True)
-        s = pd.Series(raw_cat)
-        result = s.min(skipna=True)
-        assert result == 'b'