diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index 705dac880e5..6b58ec9a8a2 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -229,6 +229,19 @@ def test_header_errors() -> None:
             pass
 
 
+@pytest.mark.parametrize("tbox", (b"", b"jp2h"))
+def test_oversized_box_length(tbox: bytes) -> None:
+    # Do not raise an OverflowError() when seeking to the end of a box,
+    # or when reading the contents of a box
+    data = (
+        b"\x00\x00\x00\x0cjP  \x0d\x0a\x87\x0a"  # JP2 signature box
+        + struct.pack(">I4s", 1, tbox)  # box with 64-bit length
+        + struct.pack(">Q", 2**63 - 12)  # oversized length
+    )
+    with pytest.raises(SyntaxError, match="Box length too large"):
+        Jpeg2KImagePlugin.Jpeg2KImageFile(BytesIO(data))
+
+
 def test_layers_type(card: ImageFile.ImageFile, tmp_path: Path) -> None:
     outfile = tmp_path / "temp_layers.jp2"
     for quality_layers in [[100, 50, 10], (100, 50, 10), None]:
diff --git a/src/PIL/Jpeg2KImagePlugin.py b/src/PIL/Jpeg2KImagePlugin.py
index ca982f06aa5..7d27fcc8fff 100644
--- a/src/PIL/Jpeg2KImagePlugin.py
+++ b/src/PIL/Jpeg2KImagePlugin.py
@@ -54,6 +54,9 @@ def _read_bytes(self, num_bytes: int) -> bytes:
         if not self._can_read(num_bytes):
             msg = "Not enough data in header"
             raise SyntaxError(msg)
+        if self.fp.tell() + num_bytes >= 2**63:
+            msg = "Box length too large"
+            raise SyntaxError(msg)
 
         data = self.fp.read(num_bytes)
         if len(data) < num_bytes:
@@ -83,6 +86,9 @@ def has_next_box(self) -> bool:
     def next_box_type(self) -> bytes:
         # Skip the rest of the box if it has not been read
         if self.remaining_in_box > 0:
+            if self.fp.tell() + self.remaining_in_box >= 2**63:
+                msg = "Box length too large"
+                raise SyntaxError(msg)
             self.fp.seek(self.remaining_in_box, os.SEEK_CUR)
         self.remaining_in_box = -1