diff --git a/Lib/test/test_mmap.py b/Lib/test/test_mmap.py
--- a/Lib/test/test_mmap.py
+++ b/Lib/test/test_mmap.py
@@ -1,11 +1,12 @@
 from test.support import (TESTFN, run_unittest, import_module, unlink,
-                          requires, _2G, _4G)
+                          requires, _2G, _4G, gc_collect)
 import unittest
 import os
 import re
 import itertools
 import socket
 import sys
+import weakref
 
 # Skip test if we can't import mmap.
 mmap = import_module('mmap')
@@ -692,6 +693,15 @@
                               "wrong exception raised in context manager")
         self.assertTrue(m.closed, "context manager failed")
 
+    def test_weakref(self):
+        # Check mmap objects are weakrefable
+        mm = mmap.mmap(-1, 16)
+        wr = weakref.ref(mm)
+        self.assertIs(wr(), mm)
+        del mm
+        gc_collect()
+        self.assertIs(wr(), None)
+
 class LargeMmapTests(unittest.TestCase):
 
     def setUp(self):
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -20,6 +20,7 @@
 
 #define PY_SSIZE_T_CLEAN
 #include <Python.h>
+#include "structmember.h"
 
 #ifndef MS_WINDOWS
 #define UNIX
@@ -108,6 +109,7 @@
     int fd;
 #endif
 
+    PyObject *weakreflist;
     access_mode access;
 } mmap_object;
 
@@ -134,6 +136,8 @@
     }
 #endif /* UNIX */
 
+    if (m_obj->weakreflist != NULL)
+        PyObject_ClearWeakRefs((PyObject *) m_obj);
     Py_TYPE(m_obj)->tp_free((PyObject*)m_obj);
 }
 
@@ -1032,7 +1036,7 @@
     0,                                          /* tp_traverse */
     0,                                          /* tp_clear */
     0,                                          /* tp_richcompare */
-    0,                                          /* tp_weaklistoffset */
+    offsetof(mmap_object, weakreflist),         /* tp_weaklistoffset */
     0,                                          /* tp_iter */
     0,                                          /* tp_iternext */
     mmap_object_methods,                        /* tp_methods */
@@ -1190,6 +1194,7 @@
     m_obj->data = NULL;
     m_obj->size = (size_t) map_size;
     m_obj->pos = (size_t) 0;
+    m_obj->weakreflist = NULL;
     m_obj->exports = 0;
     m_obj->offset = offset;
     if (fd == -1) {
@@ -1394,6 +1399,7 @@
     /* set the initial position */
     m_obj->pos = (size_t) 0;
 
+    m_obj->weakreflist = NULL;
     m_obj->exports = 0;
     /* set the tag name */
     if (tagname != NULL && *tagname != '\0') {