diff --git a/django/contrib/staticfiles/handlers.py b/django/contrib/staticfiles/handlers.py
index da53149e788..b7d9b5c18dc 100644
--- a/django/contrib/staticfiles/handlers.py
+++ b/django/contrib/staticfiles/handlers.py
@@ -99,3 +99,8 @@ class ASGIStaticFilesHandler(StaticFilesHandlerMixin, ASGIHandler):
             return await super().__call__(scope, receive, send)
         # Hand off to the main app
         return await self.application(scope, receive, send)
+
+    async def get_response_async(self, request):
+        response = await super().get_response_async(request)
+        response._resource_closers.append(request.close)
+        return response
diff --git a/django/core/handlers/asgi.py b/django/core/handlers/asgi.py
index cfe5101ea49..b5372a1d493 100644
--- a/django/core/handlers/asgi.py
+++ b/django/core/handlers/asgi.py
@@ -128,6 +128,10 @@ class ASGIRequest(HttpRequest):
     def COOKIES(self):
         return parse_cookie(self.META.get("HTTP_COOKIE", ""))
 
+    def close(self):
+        super().close()
+        self._stream.close()
+
 
 class ASGIHandler(base.BaseHandler):
     """Handler for ASGI requests."""
@@ -164,21 +168,19 @@ class ASGIHandler(base.BaseHandler):
         except RequestAborted:
             return
         # Request is complete and can be served.
-        try:
-            set_script_prefix(self.get_script_prefix(scope))
-            await sync_to_async(signals.request_started.send, thread_sensitive=True)(
-                sender=self.__class__, scope=scope
-            )
-            # Get the request and check for basic issues.
-            request, error_response = self.create_request(scope, body_file)
-            if request is None:
-                await self.send_response(error_response, send)
-                return
-            # Get the response, using the async mode of BaseHandler.
-            response = await self.get_response_async(request)
-            response._handler_class = self.__class__
-        finally:
+        set_script_prefix(self.get_script_prefix(scope))
+        await sync_to_async(signals.request_started.send, thread_sensitive=True)(
+            sender=self.__class__, scope=scope
+        )
+        # Get the request and check for basic issues.
+        request, error_response = self.create_request(scope, body_file)
+        if request is None:
             body_file.close()
+            await self.send_response(error_response, send)
+            return
+        # Get the response, using the async mode of BaseHandler.
+        response = await self.get_response_async(request)
+        response._handler_class = self.__class__
         # Increase chunk size on file responses (ASGI servers handles low-level
         # chunking).
         if isinstance(response, FileResponse):
diff --git a/django/core/handlers/wsgi.py b/django/core/handlers/wsgi.py
index 126e795fab9..1c43953717c 100644
--- a/django/core/handlers/wsgi.py
+++ b/django/core/handlers/wsgi.py
@@ -59,6 +59,9 @@ class LimitedStream:
         self.buffer = sio.read()
         return line
 
+    def close(self):
+        pass
+
 
 class WSGIRequest(HttpRequest):
     def __init__(self, environ):
diff --git a/django/http/request.py b/django/http/request.py
index 4b160bc5f4e..ad4ec0f3311 100644
--- a/django/http/request.py
+++ b/django/http/request.py
@@ -340,6 +340,8 @@ class HttpRequest:
                 self._body = self.read()
             except OSError as e:
                 raise UnreadablePostError(*e.args) from e
+            finally:
+                self._stream.close()
             self._stream = BytesIO(self._body)
         return self._body
 
diff --git a/django/test/client.py b/django/test/client.py
index 60f4c37c3f1..99e831aebda 100644
--- a/django/test/client.py
+++ b/django/test/client.py
@@ -93,6 +93,9 @@ class FakePayload:
         self.__content.write(content)
         self.__len += len(content)
 
+    def close(self):
+        pass
+
 
 def closing_iterator_wrapper(iterable, close):
     try:
diff --git a/tests/asgi/tests.py b/tests/asgi/tests.py
index cfee11802c1..57300d18fcf 100644
--- a/tests/asgi/tests.py
+++ b/tests/asgi/tests.py
@@ -165,7 +165,11 @@ class ASGITest(SimpleTestCase):
 
     async def test_post_body(self):
         application = get_asgi_application()
-        scope = self.async_request_factory._base_scope(method="POST", path="/post/")
+        scope = self.async_request_factory._base_scope(
+            method="POST",
+            path="/post/",
+            query_string="echo=1",
+        )
         communicator = ApplicationCommunicator(application, scope)
         await communicator.send_input({"type": "http.request", "body": b"Echo!"})
         response_start = await communicator.receive_output()
@@ -175,6 +179,18 @@ class ASGITest(SimpleTestCase):
         self.assertEqual(response_body["type"], "http.response.body")
         self.assertEqual(response_body["body"], b"Echo!")
 
+    async def test_untouched_request_body_gets_closed(self):
+        application = get_asgi_application()
+        scope = self.async_request_factory._base_scope(method="POST", path="/post/")
+        communicator = ApplicationCommunicator(application, scope)
+        await communicator.send_input({"type": "http.request"})
+        response_start = await communicator.receive_output()
+        self.assertEqual(response_start["type"], "http.response.start")
+        self.assertEqual(response_start["status"], 204)
+        response_body = await communicator.receive_output()
+        self.assertEqual(response_body["type"], "http.response.body")
+        self.assertEqual(response_body["body"], b"")
+
     async def test_get_query_string(self):
         application = get_asgi_application()
         for query_string in (b"name=Andrew", "name=Andrew"):
diff --git a/tests/asgi/urls.py b/tests/asgi/urls.py
index bd286c9b2fb..34595c1b6cd 100644
--- a/tests/asgi/urls.py
+++ b/tests/asgi/urls.py
@@ -26,7 +26,10 @@ def sync_waiter(request):
 
 @csrf_exempt
 def post_echo(request):
-    return HttpResponse(request.body)
+    if request.GET.get("echo"):
+        return HttpResponse(request.body)
+    else:
+        return HttpResponse(status=204)
 
 
 sync_waiter.active_threads = set()