diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 7823f74b7a153..ff3fd65b9bcea 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -41,6 +41,7 @@ Other enhancements
 - :class:`.errors.DtypeWarning` improved to include column names when mixed data types are detected (:issue:`58174`)
 - :meth:`DataFrame.cummin`, :meth:`DataFrame.cummax`, :meth:`DataFrame.cumprod` and :meth:`DataFrame.cumsum` methods now have a ``numeric_only`` parameter (:issue:`53072`)
 - :meth:`DataFrame.fillna` and :meth:`Series.fillna` can now accept ``value=None``; for non-object dtype the corresponding NA value will be used (:issue:`57723`)
+- :meth:`Series.cummin` and :meth:`Series.cummax` now supports :class:`CategoricalDtype` (:issue:`52335`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_300.notable_bug_fixes:
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 8d6880fc2acb3..6a3cf4590568c 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -6,6 +6,7 @@
 from shutil import get_terminal_size
 from typing import (
     TYPE_CHECKING,
+    Callable,
     Literal,
     cast,
     overload,
@@ -2508,6 +2509,28 @@ def equals(self, other: object) -> bool:
             return np.array_equal(self._codes, other._codes)
         return False
 
+    def _accumulate(self, name: str, skipna: bool = True, **kwargs) -> Self:
+        func: Callable
+        if name == "cummin":
+            func = np.minimum.accumulate
+        elif name == "cummax":
+            func = np.maximum.accumulate
+        else:
+            raise TypeError(f"Accumulation {name} not supported for {type(self)}")
+        self.check_for_ordered(name)
+
+        codes = self.codes.copy()
+        mask = self.isna()
+        if func == np.minimum.accumulate:
+            codes[mask] = np.iinfo(codes.dtype.type).max
+        # no need to change codes for maximum because codes[mask] is already -1
+        if not skipna:
+            mask = np.maximum.accumulate(mask)
+
+        codes = func(codes)
+        codes[mask] = -1
+        return self._simple_new(codes, dtype=self._dtype)
+
     @classmethod
     def _concat_same_type(cls, to_concat: Sequence[Self], axis: AxisInt = 0) -> Self:
         from pandas.core.dtypes.concat import union_categoricals
diff --git a/pandas/tests/series/test_cumulative.py b/pandas/tests/series/test_cumulative.py
index 9b7b08127a550..a9d5486139b46 100644
--- a/pandas/tests/series/test_cumulative.py
+++ b/pandas/tests/series/test_cumulative.py
@@ -170,6 +170,58 @@ def test_cummethods_bool_in_object_dtype(self, method, expected):
         result = getattr(ser, method)()
         tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "method, order",
+        [
+            ["cummax", "abc"],
+            ["cummin", "cba"],
+        ],
+    )
+    def test_cummax_cummin_on_ordered_categorical(self, method, order):
+        # GH#52335
+        cat = pd.CategoricalDtype(list(order), ordered=True)
+        ser = pd.Series(
+            list("ababcab"),
+            dtype=cat,
+        )
+        result = getattr(ser, method)()
+        expected = pd.Series(
+            list("abbbccc"),
+            dtype=cat,
+        )
+        tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "skip, exp",
+        [
+            [True, ["a", np.nan, "b", "b", "c"]],
+            [False, ["a", np.nan, np.nan, np.nan, np.nan]],
+        ],
+    )
+    @pytest.mark.parametrize(
+        "method, order",
+        [
+            ["cummax", "abc"],
+            ["cummin", "cba"],
+        ],
+    )
+    def test_cummax_cummin_ordered_categorical_nan(self, skip, exp, method, order):
+        # GH#52335
+        cat = pd.CategoricalDtype(list(order), ordered=True)
+        ser = pd.Series(
+            ["a", np.nan, "b", "a", "c"],
+            dtype=cat,
+        )
+        result = getattr(ser, method)(skipna=skip)
+        expected = pd.Series(
+            exp,
+            dtype=cat,
+        )
+        tm.assert_series_equal(
+            result,
+            expected,
+        )
+
     def test_cumprod_timedelta(self):
         # GH#48111
         ser = pd.Series([pd.Timedelta(days=1), pd.Timedelta(days=3)])