diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index e2a7752cf3f0d..7c826000d035a 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -8,7 +8,7 @@
 from pandas._libs import index as libindex
 from pandas._libs.lib import no_default
 from pandas._typing import ArrayLike, Label
-from pandas.util._decorators import Appender, cache_readonly, doc
+from pandas.util._decorators import Appender, doc
 
 from pandas.core.dtypes.common import (
     ensure_platform_int,
@@ -381,14 +381,6 @@ def fillna(self, value, downcast=None):
         cat = self._data.fillna(value)
         return type(self)._simple_new(cat, name=self.name)
 
-    @cache_readonly
-    def _engine(self):
-        # we are going to look things up with the codes themselves.
-        # To avoid a reference cycle, bind `codes` to a local variable, so
-        # `self` is not passed into the lambda.
-        codes = self.codes
-        return self._engine_type(lambda: codes, len(self))
-
     @doc(Index.unique)
     def unique(self, level=None):
         if level is not None: