diff --git a/azure/functions/_http_wsgi.py b/azure/functions/_http_wsgi.py
index 58c3c0e..9ed5d34 100644
--- a/azure/functions/_http_wsgi.py
+++ b/azure/functions/_http_wsgi.py
@@ -151,7 +151,12 @@ def __init__(self):
     @classmethod
     def from_app(cls, app, environ) -> 'WsgiResponse':
         res = cls()
-        res._buffer = [x or b'' for x in app(environ, res._start_response)]
+        response = app(environ, res._start_response)
+        try:
+            res._buffer = [x or b'' for x in response]
+        finally:
+            if hasattr(response, 'close'):
+                response.close()
         return res
 
     def to_func_response(self) -> HttpResponse:
diff --git a/tests/test_http_wsgi.py b/tests/test_http_wsgi.py
index d3fecec..1d465c6 100644
--- a/tests/test_http_wsgi.py
+++ b/tests/test_http_wsgi.py
@@ -5,6 +5,7 @@
 from io import StringIO, BytesIO
 
 import pytest
+from werkzeug.wsgi import ClosingIterator, FileWrapper
 
 import azure.functions as func
 from azure.functions._abc import TraceContext, RetryContext
@@ -24,6 +25,45 @@ def __init__(self, message=''):
 
 class TestHttpWsgi(unittest.TestCase):
 
+    def test_response_closes_file_wrapper(self):
+        stream = BytesIO(b'file contents')
+
+        def app(environ, start_response):
+            start_response('200 OK', [])
+            return FileWrapper(stream, buffer_size=4)
+
+        response = WsgiResponse.from_app(app, {}).to_func_response()
+        self.assertEqual(response.get_body(), b'file contents')
+        self.assertTrue(stream.closed)
+
+    def test_response_closes_empty_iterable(self):
+        closed = []
+
+        def app(environ, start_response):
+            start_response('204 No Content', [])
+            return ClosingIterator([], lambda: closed.append(True))
+
+        response = WsgiResponse.from_app(app, {}).to_func_response()
+        self.assertEqual(response.get_body(), b'')
+        self.assertEqual(closed, [True])
+
+    def test_response_closes_iterable_after_iteration_error(self):
+        closed = []
+        error = WsgiException('stream failed')
+
+        def chunks():
+            yield b'partial response'
+            raise error
+
+        def app(environ, start_response):
+            start_response('200 OK', [])
+            return ClosingIterator(chunks(), lambda: closed.append(True))
+
+        with self.assertRaises(WsgiException) as caught:
+            WsgiResponse.from_app(app, {})
+        self.assertIs(caught.exception, error)
+        self.assertEqual(closed, [True])
+
     def test_request_general_environ_conversion(self):
         func_request = self._generate_func_request()
         error_buffer = StringIO()