diff --git a/doc/source/whatsnew/v0.24.2.rst b/doc/source/whatsnew/v0.24.2.rst
index 6ad299de45e2a..c3b442e2352bb 100644
--- a/doc/source/whatsnew/v0.24.2.rst
+++ b/doc/source/whatsnew/v0.24.2.rst
@@ -49,6 +49,12 @@ Bug Fixes
 - Bug in reading a JSON with ``orient='table'`` generated by :meth:`DataFrame.to_json` with ``index=False`` (:issue:`25170`)
 - Bug where float indexes could have misaligned values when printing (:issue:`25061`)
 
+**Categorical**
+
+- Bug where calling :meth:`Series.replace` on categorical data could return a ``Series`` with incorrect dimensions (:issue:`24971`)
+-
+-
+
 **Reshaping**
 
 - Bug in :meth:`~pandas.core.groupby.GroupBy.transform` where applying a function to a timezone aware column would return a timezone naive result (:issue:`24198`)
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index e2ecb00f46df8..a61bc30a126e6 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -739,7 +739,7 @@ def copy(self, deep=True):
         values = self.values
         if deep:
             values = values.copy()
-        return self.make_block_same_class(values)
+        return self.make_block_same_class(values, ndim=self.ndim)
 
     def replace(self, to_replace, value, inplace=False, filter=None,
                 regex=False, convert=True):
diff --git a/pandas/tests/series/test_replace.py b/pandas/tests/series/test_replace.py
index 2e7b746f6c9f2..d59927993debb 100644
--- a/pandas/tests/series/test_replace.py
+++ b/pandas/tests/series/test_replace.py
@@ -281,6 +281,20 @@ def test_replace_mixed_types_with_string(self):
         expected = pd.Series([1, np.nan, 3, np.nan, 4, 5])
         tm.assert_series_equal(expected, result)
 
+    @pytest.mark.parametrize("categorical, numeric", [
+        (pd.Categorical('A', categories=['A', 'B']), [1]),
+        (pd.Categorical(('A', ), categories=['A', 'B']), [1]),
+        (pd.Categorical(('A', 'B'), categories=['A', 'B']), [1, 2]),
+    ])
+    def test_replace_categorical(self, categorical, numeric):
+        # GH 24971
+        # Do not check if dtypes are equal due to a known issue that
+        # Categorical.replace sometimes coerces to object (GH 23305)
+        s = pd.Series(categorical)
+        result = s.replace({'A': 1, 'B': 2})
+        expected = pd.Series(numeric)
+        tm.assert_series_equal(expected, result, check_dtype=False)
+
     def test_replace_with_no_overflowerror(self):
         # GH 25616
         # casts to object without Exception from OverflowError