diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 5b98b956e33e6..c085d68b36bc3 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -386,15 +386,6 @@ def fillna(self, value, downcast=None):
 
         return type(self)._simple_new(cat, name=self.name)
 
-    @doc(Index.unique)
-    def unique(self, level=None):
-        if level is not None:
-            self._validate_index_level(level)
-        result = self._values.unique()
-        # Use _simple_new instead of _shallow_copy to ensure we keep dtype
-        #  of result, not self.
-        return type(self)._simple_new(result, name=self.name)
-
     def reindex(
         self, target, method=None, level=None, limit=None, tolerance=None
     ) -> tuple[Index, np.ndarray | None]:
diff --git a/pandas/core/indexes/extension.py b/pandas/core/indexes/extension.py
index b11ec06120e0c..d28bcd6c5497a 100644
--- a/pandas/core/indexes/extension.py
+++ b/pandas/core/indexes/extension.py
@@ -331,7 +331,7 @@ def _get_unique_index(self):
             return self
 
         result = self._data.unique()
-        return self._shallow_copy(result)
+        return type(self)._simple_new(result, name=self.name)
 
     @doc(Index.map)
     def map(self, mapper, na_action=None):