diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 0f9938916b8df..1d70d27a900b1 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3286,6 +3286,11 @@ def intersection(self, other, sort: bool = False):
                 result = self.unique()._get_reconciled_name_object(other)
             else:
                 result = self._get_reconciled_name_object(other)
+
+                # Always return a new instance on equality
+                if result is self:
+                    result = self.copy()
+
             if sort is True:
                 result = result.sort_values()
             return result
diff --git a/pandas/tests/indexes/base_class/test_setops.py b/pandas/tests/indexes/base_class/test_setops.py
index d57df82b2358c..aa2f80d27ceea 100644
--- a/pandas/tests/indexes/base_class/test_setops.py
+++ b/pandas/tests/indexes/base_class/test_setops.py
@@ -264,3 +264,13 @@ def test_difference_object_type(self, diff_type, expected):
         result = getattr(idx1, diff_type)(idx2)
         expected = Index(expected)
         tm.assert_index_equal(result, expected)
+    def test_intersection_returns_new_instance(self):
+        idx1 = Index([0, 1])
+        idx2 = Index([0, 1])
+        result = idx1.intersection(idx2)
+
+        # Should be equal but NOT the same reference
+        tm.assert_index_equal(result, idx1)
+        print(idx1)
+        assert result is not idx1
+