diff --git a/asv_bench/benchmarks/index_object.py b/asv_bench/benchmarks/index_object.py
index 6541ddcb0397d..49834ae94cc38 100644
--- a/asv_bench/benchmarks/index_object.py
+++ b/asv_bench/benchmarks/index_object.py
@@ -1,3 +1,4 @@
+import gc
 import numpy as np
 import pandas.util.testing as tm
 from pandas import (
@@ -225,4 +226,21 @@ def time_intersection_both_duplicate(self, N):
         self.intv.intersection(self.intv2)
 
 
+class GC:
+    params = [1, 2, 5]
+
+    def create_use_drop(self):
+        idx = Index(list(range(1000 * 1000)))
+        idx._engine
+
+    def peakmem_gc_instances(self, N):
+        try:
+            gc.disable()
+
+            for _ in range(N):
+                self.create_use_drop()
+        finally:
+            gc.enable()
+
+
 from .pandas_vb_common import setup  # noqa: F401
diff --git a/doc/source/whatsnew/v0.25.1.rst b/doc/source/whatsnew/v0.25.1.rst
index f1d3f152e503d..443baa56374ca 100644
--- a/doc/source/whatsnew/v0.25.1.rst
+++ b/doc/source/whatsnew/v0.25.1.rst
@@ -83,6 +83,7 @@ Indexing
 ^^^^^^^^
 
 - Bug in partial-string indexing returning a NumPy array rather than a ``Series`` when indexing with a scalar like ``.loc['2015']`` (:issue:`27516`)
+- Break reference cycle involving :class:`Index` to allow garbage collection of :class:`Index` objects without running the GC. (:issue:`27585`)
 -
 -
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 17122d0981995..9297d02282a23 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -710,7 +710,11 @@ def _cleanup(self):
     @cache_readonly
     def _engine(self):
         # property, for now, slow to look up
-        return self._engine_type(lambda: self._ndarray_values, len(self))
+
+        # to avoid a refernce cycle, bind `_ndarray_values` to a local variable, so
+        # `self` is not passed into the lambda.
+        _ndarray_values = self._ndarray_values
+        return self._engine_type(lambda: _ndarray_values, len(self))
 
     # --------------------------------------------------------------------
     # Array-Like Methods
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index c40a9bce9385b..34d82525495fc 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -1,5 +1,6 @@
 from collections import defaultdict
 from datetime import datetime, timedelta
+import gc
 from io import StringIO
 import math
 import operator
@@ -2424,6 +2425,13 @@ def test_deprecated_contains(self):
             with tm.assert_produces_warning(FutureWarning):
                 index.contains(1)
 
+    def test_engine_reference_cycle(self):
+        # https://github.com/pandas-dev/pandas/issues/27585
+        index = pd.Index([1, 2, 3])
+        nrefs_pre = len(gc.get_referrers(index))
+        index._engine
+        assert len(gc.get_referrers(index)) == nrefs_pre
+
 
 class TestMixedIntIndex(Base):
     # Mostly the tests from common.py for which the results differ