diff --git a/Tests/images/zero_height.j2k b/Tests/images/zero_height.j2k
new file mode 100644
index 00000000000..21bdd8f7667
Binary files /dev/null and b/Tests/images/zero_height.j2k differ
diff --git a/Tests/test_imagefile.py b/Tests/test_imagefile.py
index 0b3aecd0849..fc0fbfb9bbc 100644
--- a/Tests/test_imagefile.py
+++ b/Tests/test_imagefile.py
@@ -2,7 +2,15 @@
 
 import pytest
 
-from PIL import BmpImagePlugin, EpsImagePlugin, Image, ImageFile, _binary, features
+from PIL import (
+    BmpImagePlugin,
+    EpsImagePlugin,
+    Image,
+    ImageFile,
+    UnidentifiedImageError,
+    _binary,
+    features,
+)
 
 from .helper import (
     assert_image,
@@ -377,3 +385,7 @@ def test_encode(self):
 
         with pytest.raises(NotImplementedError):
             encoder.encode_to_file(None, None)
+
+    def test_zero_height(self):
+        with pytest.raises(UnidentifiedImageError):
+            Image.open("Tests/images/zero_height.j2k")
diff --git a/src/PIL/ImageFile.py b/src/PIL/ImageFile.py
index 5e1dbbf683e..99b77a37f5f 100644
--- a/src/PIL/ImageFile.py
+++ b/src/PIL/ImageFile.py
@@ -123,7 +123,7 @@ def __init__(self, fp=None, filename=None):
             ) as v:
                 raise SyntaxError(v) from v
 
-            if not self.mode or self.size[0] <= 0:
+            if not self.mode or self.size[0] <= 0 or self.size[1] <= 0:
                 raise SyntaxError("not identified by this driver")
         except BaseException:
             # close the file only if we have opened it this constructor