diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 033f47f0c994d..7f983c97691ca 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -577,6 +577,7 @@ Deprecations
 - :meth:`Index.is_integer` has been deprecated. Use :func:`pandas.api.types.is_integer_dtype` instead (:issue:`50042`)
 - :meth:`Index.is_floating` has been deprecated. Use :func:`pandas.api.types.is_float_dtype` instead (:issue:`50042`)
 - :meth:`Index.holds_integer` has been deprecated. Use :func:`pandas.api.types.infer_dtype` instead (:issue:`50243`)
+- :meth:`Index.is_categorical` has been deprecated. Use :func:`pandas.api.types.is_categorical_dtype` instead (:issue:`50042`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_200.prior_deprecations:
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 7d5a7ac5945d6..9f86e5276b0d6 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2250,7 +2250,7 @@ def is_integer(self) -> bool:
         is_floating : Check if the Index is a floating type (deprecated).
         is_numeric : Check if the Index only consists of numeric data.
         is_object : Check if the Index is of the object dtype.
-        is_categorical : Check if the Index holds categorical data.
+        is_categorical : Check if the Index holds categorical data (deprecated).
         is_interval : Check if the Index holds Interval objects.
 
         Examples
@@ -2298,7 +2298,7 @@ def is_floating(self) -> bool:
         is_integer : Check if the Index only consists of integers (deprecated).
         is_numeric : Check if the Index only consists of numeric data.
         is_object : Check if the Index is of the object dtype.
-        is_categorical : Check if the Index holds categorical data.
+        is_categorical : Check if the Index holds categorical data (deprecated).
         is_interval : Check if the Index holds Interval objects.
 
         Examples
@@ -2343,7 +2343,7 @@ def is_numeric(self) -> bool:
         is_integer : Check if the Index only consists of integers (deprecated).
         is_floating : Check if the Index is a floating type (deprecated).
         is_object : Check if the Index is of the object dtype.
-        is_categorical : Check if the Index holds categorical data.
+        is_categorical : Check if the Index holds categorical data (deprecated).
         is_interval : Check if the Index holds Interval objects.
 
         Examples
@@ -2386,7 +2386,7 @@ def is_object(self) -> bool:
         is_integer : Check if the Index only consists of integers (deprecated).
         is_floating : Check if the Index is a floating type (deprecated).
         is_numeric : Check if the Index only consists of numeric data.
-        is_categorical : Check if the Index holds categorical data.
+        is_categorical : Check if the Index holds categorical data (deprecated).
         is_interval : Check if the Index holds Interval objects.
 
         Examples
@@ -2415,6 +2415,9 @@ def is_categorical(self) -> bool:
         """
         Check if the Index holds categorical data.
 
+        .. deprecated:: 2.0.0
+              Use :meth:`pandas.api.types.is_categorical_dtype` instead.
+
         Returns
         -------
         bool
@@ -2451,6 +2454,13 @@ def is_categorical(self) -> bool:
         >>> s.index.is_categorical()
         False
         """
+        warnings.warn(
+            f"{type(self).__name__}.is_categorical is deprecated."
+            "Use pandas.api.types.is_categorical_dtype instead",
+            FutureWarning,
+            stacklevel=find_stack_level(),
+        )
+
         return self.inferred_type in ["categorical"]
 
     @final
@@ -2471,7 +2481,7 @@ def is_interval(self) -> bool:
         is_floating : Check if the Index is a floating type (deprecated).
         is_numeric : Check if the Index only consists of numeric data.
         is_object : Check if the Index is of the object dtype.
-        is_categorical : Check if the Index holds categorical data.
+        is_categorical : Check if the Index holds categorical data (deprecated).
 
         Examples
         --------
@@ -5033,7 +5043,11 @@ def _can_hold_identifiers_and_holds_name(self, name) -> bool:
 
         https://github.com/pandas-dev/pandas/issues/19764
         """
-        if self.is_object() or is_string_dtype(self.dtype) or self.is_categorical():
+        if (
+            self.is_object()
+            or is_string_dtype(self.dtype)
+            or is_categorical_dtype(self.dtype)
+        ):
             return name in self
         return False
 
diff --git a/pandas/tests/indexes/common.py b/pandas/tests/indexes/common.py
index ed8eb350234d1..779c1cc6ccd05 100644
--- a/pandas/tests/indexes/common.py
+++ b/pandas/tests/indexes/common.py
@@ -822,6 +822,15 @@ def test_holds_integer_deprecated(self, simple_index):
         with tm.assert_produces_warning(FutureWarning, match=msg):
             idx.holds_integer()
 
+    def test_is_categorical_is_deprecated(self, simple_index):
+        # GH50042
+        idx = simple_index
+        with tm.assert_produces_warning(
+            FutureWarning,
+            match=r"Use pandas\.api\.types\.is_categorical_dtype instead",
+        ):
+            idx.is_categorical()
+
 
 class NumericBase(Base):
     """