diff --git a/synapse/http/site.py b/synapse/http/site.py
index 1cd90cb9b7..e83a4447b2 100644
--- a/synapse/http/site.py
+++ b/synapse/http/site.py
@@ -21,6 +21,7 @@
 import contextlib
 import logging
 import time
+from http import HTTPStatus
 from typing import TYPE_CHECKING, Any, Generator, Optional, Tuple, Union
 
 import attr
@@ -139,6 +140,41 @@ class SynapseRequest(Request):
             self.synapse_site.site_tag,
         )
 
+    # Twisted machinery: this method is called by the Channel once the full request has
+    # been received, to dispatch the request to a resource.
+    #
+    # We're patching Twisted to bail/abort early when we see someone trying to upload
+    # `multipart/form-data` so we can avoid Twisted parsing the entire request body into
+    # in-memory (specific problem of this specific `Content-Type`). This protects us
+    # from an attacker uploading something bigger than the available RAM and crashing
+    # the server with a `MemoryError`, or carefully block just enough resources to cause
+    # all other requests to fail.
+    #
+    # FIXME: This can be removed once we Twisted releases a fix and we update to a
+    # version that is patched
+    def requestReceived(self, command: bytes, path: bytes, version: bytes) -> None:
+        if command == b"POST":
+            ctype = self.requestHeaders.getRawHeaders(b"content-type")
+            if ctype and b"multipart/form-data" in ctype[0]:
+                self.method, self.uri = command, path
+                self.clientproto = version
+                self.code = HTTPStatus.UNSUPPORTED_MEDIA_TYPE.value
+                self.code_message = bytes(
+                    HTTPStatus.UNSUPPORTED_MEDIA_TYPE.phrase, "ascii"
+                )
+                self.responseHeaders.setRawHeaders(b"content-length", [b"0"])
+
+                logger.warning(
+                    "Aborting connection from %s because `content-type: multipart/form-data` is unsupported: %s %s",
+                    self.client,
+                    command,
+                    path,
+                )
+                self.write(b"")
+                self.loseConnection()
+                return
+        return super().requestReceived(command, path, version)
+
     def handleContentChunk(self, data: bytes) -> None:
         # we should have a `content` by now.
         assert self.content, "handleContentChunk() called before gotLength()"
diff --git a/tests/http/test_site.py b/tests/http/test_site.py
index bfa26a329c..fc620c705a 100644
--- a/tests/http/test_site.py
+++ b/tests/http/test_site.py
@@ -90,3 +90,56 @@ class SynapseRequestTestCase(HomeserverTestCase):
         # default max upload size is 50M, so it should drop on the next buffer after
         # that.
         self.assertEqual(sent, 50 * 1024 * 1024 + 1024)
+
+    def test_content_type_multipart(self) -> None:
+        """HTTP POST requests with `content-type: multipart/form-data` should be rejected"""
+        self.hs.start_listening()
+
+        # find the HTTP server which is configured to listen on port 0
+        (port, factory, _backlog, interface) = self.reactor.tcpServers[0]
+        self.assertEqual(interface, "::")
+        self.assertEqual(port, 0)
+
+        # as a control case, first send a regular request.
+
+        # complete the connection and wire it up to a fake transport
+        client_address = IPv6Address("TCP", "::1", 2345)
+        protocol = factory.buildProtocol(client_address)
+        transport = StringTransport()
+        protocol.makeConnection(transport)
+
+        protocol.dataReceived(
+            b"POST / HTTP/1.1\r\n"
+            b"Connection: close\r\n"
+            b"Transfer-Encoding: chunked\r\n"
+            b"\r\n"
+            b"0\r\n"
+            b"\r\n"
+        )
+
+        while not transport.disconnecting:
+            self.reactor.advance(1)
+
+        # we should get a 404
+        self.assertRegex(transport.value().decode(), r"^HTTP/1\.1 404 ")
+
+        # now send request with content-type header
+        protocol = factory.buildProtocol(client_address)
+        transport = StringTransport()
+        protocol.makeConnection(transport)
+
+        protocol.dataReceived(
+            b"POST / HTTP/1.1\r\n"
+            b"Connection: close\r\n"
+            b"Transfer-Encoding: chunked\r\n"
+            b"Content-Type: multipart/form-data\r\n"
+            b"\r\n"
+            b"0\r\n"
+            b"\r\n"
+        )
+
+        while not transport.disconnecting:
+            self.reactor.advance(1)
+
+        # we should get a 415
+        self.assertRegex(transport.value().decode(), r"^HTTP/1\.1 415 ")