diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index ff3879018674e..0b000363b5988 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -7190,6 +7190,63 @@ def __invert__(self) -> Index:
         # GH#8875
         return self._unary_method(operator.inv)
 
+    # --------------------------------------------------------------------
+    # String Case Conversion Methods
+
+    def to_snake_case(self):
+        """
+        Convert index labels to snake_case.
+
+        Returns
+        -------
+        Index
+            A new Index with labels converted to snake_case.
+
+        Notes
+        -----
+        This method uses the `inflection.underscore` function to perform the
+        conversion. Non-string values in the index are left unchanged.
+
+        Examples
+        --------
+        >>> idx = pd.Index(["ColumnName", "AnotherColumn", 123])
+        >>> idx.to_snake_case()
+        Index(['column_name', 'another_column', 123], dtype='object')
+        """
+        from inflection import underscore
+
+        return self.map(
+            lambda x: underscore(x.replace(" ", "_")) if isinstance(x, str) else x
+        )
+
+    def to_camel_case(self):
+        """
+        Convert index labels to camelCase.
+
+        Returns
+        -------
+        Index
+            A new Index with labels converted to camelCase.
+
+        Notes
+        -----
+        This method uses the `inflection.camelize` function to perform the
+        conversion. Non-string values in the index are left unchanged.
+
+        Examples
+        --------
+        >>> idx = pd.Index(["column_name", "another_column", 123])
+        >>> idx.to_camel_case()
+        Index(['columnName', 'anotherColumn', 123], dtype='object')
+        """
+        from inflection import camelize
+
+        return self.map(
+            lambda x: camelize(x.replace(" ", "_"), uppercase_first_letter=False)
+            if isinstance(x, str)
+            else x
+        )
+
     # --------------------------------------------------------------------
     # Reductions
 
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 5b75bd9afd6df..5dedbe165f774 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -1350,6 +1350,38 @@ def test_index_round(self, decimals, expected_results):
 
         tm.assert_index_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "input_labels, expected_snake_case",
+        [
+            (
+                ["ColumnName", "AnotherColumn", 123],
+                ["column_name", "another_column", 123],
+            ),
+            (["MixedCase", "with spaces", None], ["mixed_case", "with_spaces", None]),
+        ],
+    )
+    def test_to_snake_case(self, input_labels, expected_snake_case):
+        idx = Index(input_labels)
+        result = idx.to_snake_case()
+        expected = Index(expected_snake_case)
+        tm.assert_index_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "input_labels, expected_camel_case",
+        [
+            (
+                ["column_name", "another_column", 123],
+                ["columnName", "anotherColumn", 123],
+            ),
+            (["with_spaces", "Mixed_Case", None], ["withSpaces", "mixedCase", None]),
+        ],
+    )
+    def test_to_camel_case(self, input_labels, expected_camel_case):
+        idx = Index(input_labels)
+        result = idx.to_camel_case()
+        expected = Index(expected_camel_case)
+        tm.assert_index_equal(result, expected)
+
 
 class TestMixedIntIndex:
     # Mostly the tests from common.py for which the results differ