diff --git a/PIL/Image.py b/PIL/Image.py
index 2f304a9a8..58944f891 100644
--- a/PIL/Image.py
+++ b/PIL/Image.py
@@ -109,6 +109,7 @@ from PIL._util import deferred_error
 
 import os
 import sys
+import io
 
 # type stuff
 import collections
@@ -2248,6 +2249,11 @@ def open(fp, mode="r"):
     else:
         filename = ""
 
+    try:
+        fp.seek(0)
+    except (AttributeError, io.UnsupportedOperation):
+        fp = io.BytesIO(fp.read())
+
     prefix = fp.read(16)
 
     preinit()