diff --git a/Lib/test/test_zipfile/test_core.py b/Lib/test/test_zipfile/test_core.py
@@ -4319,6 +4319,41 @@ def test_negative_central_directory_offset_raises_BadZipFile(self):
             f = io.BytesIO(buffer)
             self.assertRaises(zipfile.BadZipFile, zipfile.ZipFile, f)
 
+    def test_negative_file_header_offset_raises_BadZipFile(self):
+        data = io.BytesIO()
+        with zipfile.ZipFile(data, "w") as zipf:
+            zipf.writestr("bad.txt", b"corrupt header")
+            zipf.writestr("good.txt", b"intact contents")
+        # Removing the first byte leaves the central directory intact, but
+        # makes the first member's local file header offset negative.
+        damaged = data.getvalue()[1:]
+        for file in get_files(self):
+            with self.subTest(type=type(file)):
+                if isinstance(file, str):
+                    with open(file, "wb") as fp:
+                        fp.write(damaged)
+                else:
+                    file.write(damaged)
+                    file.seek(0)
+                with zipfile.ZipFile(file) as zipf:
+                    for name in ("bad.txt", zipf.getinfo("bad.txt")):
+                        with self.assertRaises(zipfile.BadZipFile):
+                            zipf.open(name)
+                    self.assertEqual(zipf.testzip(), "bad.txt")
+                    self.assertEqual(zipf.read("good.txt"), b"intact contents")
+
+    def test_read_file_header_raises_OSError(self):
+        data = io.BytesIO()
+        with zipfile.ZipFile(data, "w") as zipf:
+            zipf.writestr("foo.txt", b"contents")
+        data.seek(0)
+        with zipfile.ZipFile(data) as zipf:
+            with mock.patch.object(data, "seek", side_effect=OSError("seek failed")):
+                with self.assertRaisesRegex(OSError, "seek failed"):
+                    zipf.read("foo.txt")
+                with self.assertRaisesRegex(OSError, "seek failed"):
+                    zipf.testzip()
+
     def test_closed_zip_raises_ValueError(self):
         """Verify that testzip() doesn't swallow inappropriate exceptions."""
         data = io.BytesIO()

diff --git a/Lib/zipfile/__init__.py b/Lib/zipfile/__init__.py
@@ -2243,6 +2243,8 @@ def open(self, name, mode="r", pwd=None, *, force_zip64=False):
                     "Close the writing handle before trying to read.")
 
         # Open for reading:
+        if zinfo.header_offset < 0:
+            raise BadZipFile("Bad offset for file header")
         self._fileRefCnt += 1
         zef_file = _SharedFile(self.fp, zinfo.header_offset,
                                self._fpclose, self._lock, lambda: self._writing)

diff --git a/Misc/NEWS.d/next/Library/2026-10-06-14-17-00.gh-issue-91087.qZ3rTp.rst b/Misc/NEWS.d/next/Library/2026-10-06-14-17-00.gh-issue-91087.qZ3rTp.rst
@@ -0,0 +1,4 @@
+:meth:`zipfile.ZipFile.open` now raises :exc:`~zipfile.BadZipFile` for negative
+file header offsets in corrupted archives. :meth:`~zipfile.ZipFile.testzip`
+reports the affected member instead of raising an :exc:`OSError` or
+:exc:`ValueError`.