diff --git a/cachecontrol/adapter.py b/cachecontrol/adapter.py
index e739a480..9a326349 100644
--- a/cachecontrol/adapter.py
+++ b/cachecontrol/adapter.py
@@ -5,6 +5,7 @@
 
 import functools
 import types
+import weakref
 import zlib
 from typing import TYPE_CHECKING, Any, Collection, Mapping
 
@@ -128,19 +129,25 @@ def build_response(  # type: ignore[override]
                 response._fp = CallbackFileWrapper(  # type: ignore[assignment]
                     response._fp,  # type: ignore[arg-type]
                     functools.partial(
-                        self.controller.cache_response, request, response
+                        self.controller.cache_response, request, weakref.ref(response)
                     ),
                 )
                 if response.chunked:
-                    super_update_chunk_length = response._update_chunk_length
+                    super_update_chunk_length = response.__class__._update_chunk_length
 
-                    def _update_chunk_length(self: HTTPResponse) -> None:
-                        super_update_chunk_length()
+                    def _update_chunk_length(
+                        weak_self: weakref.ReferenceType[HTTPResponse],
+                    ) -> None:
+                        self = weak_self()
+                        if self is None:
+                            return
+
+                        super_update_chunk_length(self)
                         if self.chunk_left == 0:
                             self._fp._close()  # type: ignore[union-attr]
 
-                    response._update_chunk_length = types.MethodType(  # type: ignore[method-assign]
-                        _update_chunk_length, response
+                    response._update_chunk_length = functools.partial(  # type: ignore[method-assign]
+                        _update_chunk_length, weakref.ref(response)
                     )
 
         resp: Response = super().build_response(request, response)
diff --git a/cachecontrol/controller.py b/cachecontrol/controller.py
index f826aec0..4e251c8f 100644
--- a/cachecontrol/controller.py
+++ b/cachecontrol/controller.py
@@ -12,6 +12,7 @@
 import logging
 import re
 import time
+import weakref
 from email.utils import parsedate_tz
 from typing import TYPE_CHECKING, Collection, Mapping
 
@@ -323,7 +324,7 @@ def _cache_set(
     def cache_response(
         self,
         request: PreparedRequest,
-        response: HTTPResponse,
+        response_or_ref: HTTPResponse | weakref.ReferenceType[HTTPResponse],
         body: bytes | None = None,
         status_codes: Collection[int] | None = None,
     ) -> None:
@@ -332,6 +333,16 @@ def cache_response(
 
         This assumes a requests Response object.
         """
+        if isinstance(response_or_ref, weakref.ReferenceType):
+            response = response_or_ref()
+            if response is None:
+                # The weakref can be None only in case the user used streamed request
+                # and did not consume or close it, and holds no reference to requests.Response.
+                # In such case, we don't want to cache the response.
+                return
+        else:
+            response = response_or_ref
+
         # From httplib2: Don't cache 206's since we aren't going to
         #                handle byte range requests
         cacheable_status_codes = status_codes or self.cacheable_status_codes
diff --git a/tests/test_adapter.py b/tests/test_adapter.py
index 2614e098..7fd0c59e 100644
--- a/tests/test_adapter.py
+++ b/tests/test_adapter.py
@@ -2,10 +2,13 @@
 #
 # SPDX-License-Identifier: Apache-2.0
 
+import gc
+import weakref
 from unittest import mock
-import pytest
 
+import pytest
 from requests import Session
+
 from cachecontrol.adapter import CacheControlAdapter
 from cachecontrol.cache import DictCache
 from cachecontrol.wrapper import CacheControl
@@ -65,3 +68,22 @@ def test_close(self):
 
         sess.close()
         assert cache.close.called
+
+    def test_do_not_leak_response(self, url, sess):
+        resp = sess.get(url + "stream", stream=True)
+        resp.raise_for_status()
+        r1_weak = weakref.ref(resp.raw)
+
+        # This is a mis-use of requests, becase we should either consume
+        # the body, or call .close().
+        # But requests without cachecontrol handle this anyway, because
+        # urllib3.response.HTTPResponse has a __del__ finalizer on it that closes it
+        # once there are no more references to it.
+        # We should not break this.
+
+        resp = None
+        # Below this point, it should be closed because there are no more references
+        # to the session response.
+
+        r1 = r1_weak()
+        assert r1 is None or r1.closed