diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index d1b965e64e43b..01aad7eae4d79 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -314,7 +314,7 @@ Other enhancements
 - Added new argument ``engine`` to :func:`read_json` to support parsing JSON with pyarrow by specifying ``engine="pyarrow"`` (:issue:`48893`)
 - Added support for SQLAlchemy 2.0 (:issue:`40686`)
 - :class:`Index` set operations :meth:`Index.union`, :meth:`Index.intersection`, :meth:`Index.difference`, and :meth:`Index.symmetric_difference` now support ``sort=True``, which will always return a sorted result, unlike the default ``sort=None`` which does not sort in some cases (:issue:`25151`)
--
+- Added :meth:`Index.filter` that allows filtering on :class:`Index` to create a new :class:`Index` object
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_200.notable_bug_fixes:
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index d76648558bc6e..0938dcb97b7ff 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -5473,6 +5473,8 @@ def filter(
         --------
         DataFrame.loc : Access a group of rows and columns
             by label(s) or a boolean array.
+        Index.filter : Create a subset of the index according to the specified index
+            labels.
 
         Notes
         -----
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 8adb7cca45323..742c8952bd957 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4,6 +4,7 @@
 import functools
 from itertools import zip_longest
 import operator
+import re
 from typing import (
     TYPE_CHECKING,
     Any,
@@ -88,6 +89,7 @@
     ensure_int64,
     ensure_object,
     ensure_platform_int,
+    ensure_str,
     is_any_real_numeric_dtype,
     is_bool_dtype,
     is_categorical_dtype,
@@ -155,6 +157,7 @@
     PandasObject,
 )
 import pandas.core.common as com
+from pandas.core.common import count_not_none
 from pandas.core.construction import (
     ensure_wrapped_if_datetimelike,
     extract_array,
@@ -6150,6 +6153,76 @@ def map(self, mapper, na_action=None):
 
         return Index._with_infer(new_values, dtype=dtype, copy=False, name=self.name)
 
+    def filter(
+        self: _IndexT,
+        items: Axes | None = None,
+        like: str_t | None = None,
+        regex: str_t | None = None,
+    ) -> _IndexT:
+        """
+        Create a subset of the index according to the specified index labels.
+
+        Parameters
+        ----------
+        items : list-like
+            Keep labels from index which are in items.
+        like : str
+            Keep labels from index for which "like in label == True".
+        regex : str (regular expression)
+            Keep labels from index for which re.search(regex, label) == True.
+
+        Returns
+        -------
+        same type as input object
+
+        See Also
+        --------
+        DataFrame.filter : Subset the dataframe rows or columns according to the
+            specified index labels.
+
+        Notes
+        -----
+        The ``items``, ``like``, and ``regex`` parameters are
+        enforced to be mutually exclusive.
+
+        Examples
+        --------
+        >>> idx = pd.Index(["cat", "dog", "bat", "bird"])
+        >>> idx
+        Index(['cat', 'dog', 'bat', 'bird'], dtype='object')
+
+        >>> # select index values by name
+        >>> idx.filter(items=['cat', 'dog'])
+        Index(['cat', 'dog'], dtype='object')
+
+        >>> # select index values by regular expression
+        >>> idx.filter(regex=r'b.*')
+        Index(['bat', 'bird'], dtype='object')
+
+        >>> # select index values containing 'at'
+        >>> idx.filter(like='at')
+        Index(['cat', 'bat'], dtype='object')
+        """
+        nkw = count_not_none(items, like, regex)
+        if nkw > 1:
+            raise TypeError(
+                "Keyword arguments `items`, `like`, or `regex` "
+                "are mutually exclusive"
+            )
+
+        if items is not None:
+            mask = [r in items for r in self]
+        elif like:
+            mask = [like in ensure_str(r) for r in self]
+        elif regex:
+            matcher = re.compile(regex)
+            mask = [matcher.search(ensure_str(r)) is not None for r in self]
+        else:
+            raise TypeError("Must pass either `items`, `like`, or `regex`")
+        boolmask = np.array(mask, dtype=np.bool_)
+        res_values = self._data[boolmask]
+        return type(self)._simple_new(res_values, name=self._name)
+
     # TODO: De-duplicate with map, xref GH#32349
     @final
     def _transform_index(self, func, *, level=None) -> Index:
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 783cf76403059..ae1f51efcf723 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -1285,6 +1285,34 @@ def test_sortlevel(self):
         result = index.sortlevel(ascending=False)
         tm.assert_index_equal(result[0], expected)
 
+    @pytest.mark.parametrize(
+        "dtype",
+        ["object", pd.StringDtype()],
+    )
+    def test_filter_string(self, dtype):
+        idx = Index(["cat", "dog", "bat", "bird"], dtype=dtype)
+        result = idx.filter(["cat", "dog"])
+        expected = Index(["cat", "dog"], dtype=dtype)
+        tm.assert_index_equal(result, expected)
+
+        result = idx.filter(like="at")
+        expected = Index(["cat", "bat"], dtype=dtype)
+        tm.assert_index_equal(result, expected)
+
+        result = idx.filter(regex=r"b.*")
+        expected = Index(["bat", "bird"], dtype=dtype)
+        tm.assert_index_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "dtype",
+        ["int", pd.Int64Dtype()],
+    )
+    def test_filter_int(self, dtype):
+        idx = Index([1, 2, 3, 4, 5], dtype=dtype)
+        result = idx.filter(range(2, 4))
+        expected = Index([2, 3], dtype=dtype)
+        tm.assert_index_equal(result, expected)
+
 
 class TestMixedIntIndex(Base):
     # Mostly the tests from common.py for which the results differ