diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 7ec50137c3039..7f0a5f77d0905 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -1064,6 +1064,8 @@ Reshaping
 - Bug in :meth:`concat` where concatenating DataFrame and Series with ``ignore_index = True`` drops the series name (:issue:`60723`, :issue:`56257`)
 - Bug in :func:`melt` where calling with duplicate column names in ``id_vars`` raised a misleading ``AttributeError`` (:issue:`61475`)
 - Bug in :meth:`DataFrame.merge` where user-provided suffixes could result in duplicate column names if the resulting names matched existing columns. Now raises a :class:`MergeError` in such cases. (:issue:`61402`)
+- Bug in :meth:`DataFrame.merge` with :class:`CategoricalDtype` columns incorrectly raising ``RecursionError`` (:issue:`56376`)
+-
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 3bd35a6dfed29..a3634e370cfc3 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -1727,6 +1727,17 @@ def np_can_hold_element(dtype: np.dtype, element: Any) -> Any:
 
         if tipo is not None:
             # TODO: itemsize check?
+
+            if isinstance(tipo, CategoricalDtype):
+                # GH#56376
+                if tipo.categories.dtype.kind not in "iuf":
+                    # Anything other than float/integer we cannot hold
+                    raise LossySetitemError
+                casted = np.asarray(element, dtype=dtype)
+                if np.array_equal(casted, element, equal_nan=True):
+                    return casted
+                raise LossySetitemError
+
             if tipo.kind not in "iuf":
                 # Anything other than float/integer we cannot hold
                 raise LossySetitemError
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 55dfb41b8c894..26d297b86954d 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5386,6 +5386,12 @@ def putmask(self, mask, value) -> Index:
 
             # See also: Block.coerce_to_target_dtype
             dtype = self._find_common_type_compat(value)
+            if dtype == self.dtype:
+                # GH#56376 avoid RecursionError
+                raise AssertionError(
+                    "Something has gone wrong. Please report a bug at "
+                    "github.com/pandas-dev/pandas"
+                ) from err
             return self.astype(dtype).putmask(mask, value)
 
         values = self._values.copy()
diff --git a/pandas/tests/dtypes/cast/test_can_hold_element.py b/pandas/tests/dtypes/cast/test_can_hold_element.py
index 5ef021753b843..b833c601ec2c8 100644
--- a/pandas/tests/dtypes/cast/test_can_hold_element.py
+++ b/pandas/tests/dtypes/cast/test_can_hold_element.py
@@ -2,6 +2,8 @@
 
 from pandas.core.dtypes.cast import can_hold_element
 
+from pandas import Categorical
+
 
 def test_can_hold_element_range(any_int_numpy_dtype):
     # GH#44261
@@ -96,3 +98,11 @@ def test_can_hold_element_bool():
     assert not can_hold_element(arr, element)
     assert not can_hold_element(arr, np.array([element]))
     assert not can_hold_element(arr, np.array([element], dtype=object))
+
+
+def test_can_hold_element_categorical():
+    # GH#56376
+    arr = np.array([], dtype=np.float64)
+    cat = Categorical([1, 2, None])
+
+    assert can_hold_element(arr, cat)
diff --git a/pandas/tests/reshape/merge/test_merge.py b/pandas/tests/reshape/merge/test_merge.py
index a8e29ef03acc2..1ddf00527196a 100644
--- a/pandas/tests/reshape/merge/test_merge.py
+++ b/pandas/tests/reshape/merge/test_merge.py
@@ -3070,3 +3070,17 @@ def test_merge_for_suffix_collisions(suffixes):
     df2 = DataFrame({"col1": [1], "col2": [2], "col2_dup": [3]})
     with pytest.raises(MergeError, match="duplicate columns"):
         merge(df1, df2, on="col1", suffixes=suffixes)
+
+
+def test_merge_categorical_key_recursion():
+    # GH#56376
+    lt = CategoricalDtype(categories=np.asarray([1, 2, 3], dtype="int64"))
+    rt = CategoricalDtype(categories=np.asarray([1, 2, 3], dtype="float64"))
+    left = DataFrame({"key": Series([1, 2], dtype=lt)})
+    right = DataFrame({"key": Series([1, 3], dtype=rt)})
+
+    result = left.merge(right, on="key", how="outer")
+    expected = left.astype("int64").merge(
+        right.astype("float64"), on="key", how="outer"
+    )
+    tm.assert_frame_equal(result, expected)