diff --git a/Tests/test_file_png.py b/Tests/test_file_png.py
index 469d186e8..3c5286ad0 100644
--- a/Tests/test_file_png.py
+++ b/Tests/test_file_png.py
@@ -635,7 +635,10 @@ class TestFilePng:
 
     def test_seek(self):
         with Image.open(TEST_PNG_FILE) as im:
+            assert im.n_frames == 1
             im.seek(0)
+            with pytest.raises(EOFError):
+                im.seek(1)
 
 
 @pytest.mark.skipif(is_win32(), reason="Requires Unix or macOS")
diff --git a/src/PIL/PngImagePlugin.py b/src/PIL/PngImagePlugin.py
index 0291df4b0..3f2a0c5e8 100644
--- a/src/PIL/PngImagePlugin.py
+++ b/src/PIL/PngImagePlugin.py
@@ -636,7 +636,6 @@ class PngImageFile(ImageFile.ImageFile):
         if self.fp.read(8) != _MAGIC:
             raise SyntaxError("not a PNG file")
         self.__fp = self.fp
-        self.__frame = 0
 
         #
         # Parse headers up to the first IDAT or fDAT chunk
@@ -685,7 +684,12 @@ class PngImageFile(ImageFile.ImageFile):
         else:
             self.__prepare_idat = length  # used by load_prepare()
 
-        if self._n_frames is not None:
+        if self._n_frames is None:
+            # standard PNG image, frame-related attributes still need to be
+            # initialized for seek()/_seek_check() to behave as expected
+            self.__frame = 0
+            self._n_frames = 1
+        else:
             self._close_exclusive_fp_after_loading = False
             self.png.save_rewind()
             self.__rewind_idat = self.__prepare_idat