diff --git a/Tests/images/sugarshack_no_data.mpo b/Tests/images/sugarshack_no_data.mpo
new file mode 100644
index 000000000..d94bad53b
Binary files /dev/null and b/Tests/images/sugarshack_no_data.mpo differ
diff --git a/Tests/test_file_mpo.py b/Tests/test_file_mpo.py
index 9c8a2b468..cdcf2b041 100644
--- a/Tests/test_file_mpo.py
+++ b/Tests/test_file_mpo.py
@@ -113,6 +113,13 @@ class TestFileMpo(PillowTestCase):
             self.assertEqual(mpinfo[45056], b"0100")
             self.assertEqual(mpinfo[45057], 2)
 
+    def test_mp_no_data(self):
+        # This image has been manually hexedited to have the second frame
+        # beyond the end of the file
+        with Image.open("Tests/images/sugarshack_no_data.mpo") as im:
+            with self.assertRaises(ValueError):
+                im.seek(1)
+
     def test_mp_attribute(self):
         for test_file in test_files:
             with Image.open(test_file) as im:
diff --git a/src/PIL/MpoImagePlugin.py b/src/PIL/MpoImagePlugin.py
index a63e76fe7..e97176d57 100644
--- a/src/PIL/MpoImagePlugin.py
+++ b/src/PIL/MpoImagePlugin.py
@@ -82,7 +82,10 @@ class MpoImageFile(JpegImagePlugin.JpegImageFile):
         self.offset = self.__mpoffsets[frame]
 
         self.fp.seek(self.offset + 2)  # skip SOI marker
-        if i16(self.fp.read(2)) == 0xFFE1:  # APP1
+        segment = self.fp.read(2)
+        if not segment:
+            raise ValueError("No data found for frame")
+        if i16(segment) == 0xFFE1:  # APP1
             n = i16(self.fp.read(2)) - 2
             self.info["exif"] = ImageFile._safe_read(self.fp, n)