diff --git a/django/http/response.py b/django/http/response.py
index 04efbd6bef..c39519c4bb 100644
--- a/django/http/response.py
+++ b/django/http/response.py
@@ -241,6 +241,9 @@ class HttpResponseBase:
 
     # The WSGI server must call this method upon completion of the request.
     # See http://blog.dscpl.com.au/2012/10/obligations-for-calling-close-on.html
+    # When wsgi.file_wrapper is used, the WSGI server instead calls close()
+    # on the file-like object. Django ensures this method is called in this
+    # case by replacing self.file_to_stream.close() with a wrapped version.
     def close(self):
         for closable in self._closable_objects:
             try:
@@ -397,14 +400,39 @@ class FileResponse(StreamingHttpResponse):
         self.filename = filename
         super().__init__(*args, **kwargs)
 
+    def _wrap_file_to_stream_close(self, filelike):
+        """
+        Wrap the file-like close() with a version that calls
+        FileResponse.close().
+        """
+        closing = False
+        filelike_close = getattr(filelike, 'close', lambda: None)
+
+        def file_wrapper_close():
+            nonlocal closing
+            # Prevent an infinite loop since FileResponse.close() tries to
+            # close the objects in self._closable_objects.
+            if closing:
+                return
+            closing = True
+            try:
+                filelike_close()
+            finally:
+                self.close()
+
+        filelike.close = file_wrapper_close
+
     def _set_streaming_content(self, value):
         if not hasattr(value, 'read'):
             self.file_to_stream = None
             return super()._set_streaming_content(value)
 
         self.file_to_stream = filelike = value
+        # Add to closable objects before wrapping close(), since the filelike
+        # might not have close().
         if hasattr(filelike, 'close'):
             self._closable_objects.append(filelike)
+        self._wrap_file_to_stream_close(filelike)
         value = iter(lambda: filelike.read(self.block_size), b'')
         self.set_headers(filelike)
         super()._set_streaming_content(value)
diff --git a/docs/ref/request-response.txt b/docs/ref/request-response.txt
index 07dc42900d..8e0928654d 100644
--- a/docs/ref/request-response.txt
+++ b/docs/ref/request-response.txt
@@ -861,7 +861,8 @@ Methods
 .. method:: HttpResponse.close()
 
     This method is called at the end of the request directly by the WSGI
-    server.
+    server, or when the WSGI server closes the file-like object, if
+    `wsgi.file_wrapper`_ is used for the request.
 
 .. method:: HttpResponse.write(content)
 
diff --git a/tests/responses/test_fileresponse.py b/tests/responses/test_fileresponse.py
index e77df4513a..a6bcb58466 100644
--- a/tests/responses/test_fileresponse.py
+++ b/tests/responses/test_fileresponse.py
@@ -80,3 +80,52 @@ class FileResponseTests(SimpleTestCase):
             response['Content-Disposition'],
             "attachment; filename*=utf-8''%E7%A5%9D%E6%82%A8%E5%B9%B3%E5%AE%89.odt"
         )
+
+    def test_file_to_stream_closes_response(self):
+        # Closing file_to_stream calls FileResponse.close(), even when
+        # file-like object doesn't have a close() method.
+        class FileLike:
+            def read(self):
+                pass
+
+        class FileLikeWithClose(FileLike):
+            def __init__(self):
+                self.closed = False
+
+            def close(self):
+                self.closed = True
+
+        for filelike_cls in (FileLike, FileLikeWithClose):
+            with self.subTest(filelike_cls=filelike_cls.__name__):
+                filelike = filelike_cls()
+                response = FileResponse(filelike)
+                self.assertFalse(response.closed)
+                # Object with close() is added to the list of closable.
+                if hasattr(filelike, 'closed'):
+                    self.assertEqual(response._closable_objects, [filelike])
+                else:
+                    self.assertEqual(response._closable_objects, [])
+                file_to_stream = response.file_to_stream
+                file_to_stream.close()
+                if hasattr(filelike, 'closed'):
+                    self.assertTrue(filelike.closed)
+                self.assertTrue(response.closed)
+
+    def test_file_to_stream_closes_response_on_error(self):
+        # Closing file_to_stream calls FileResponse.close(), even when
+        # closing file-like raises exceptions.
+        class FileLikeWithRaisingClose:
+            def read(self):
+                pass
+
+            def close(self):
+                raise RuntimeError()
+
+        filelike = FileLikeWithRaisingClose()
+        response = FileResponse(filelike)
+        self.assertFalse(response.closed)
+        self.assertEqual(response._closable_objects, [filelike])
+        file_to_stream = response.file_to_stream
+        with self.assertRaises(RuntimeError):
+            file_to_stream.close()
+        self.assertTrue(response.closed)