diff --git a/gunicorn/http/wsgi.py b/gunicorn/http/wsgi.py
index 1d48467d1..b85762589 100644
--- a/gunicorn/http/wsgi.py
+++ b/gunicorn/http/wsgi.py
@@ -355,7 +355,7 @@ def sendfile(self, respiter):
 
         try:
             fileno = respiter.filelike.fileno()
-        except AttributeError:
+        except (AttributeError, io.UnsupportedOperation):
             return False
 
         try: