diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 8a4f74de4f3e58..a3dbf1b1a7b94f 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -453,8 +453,12 @@ def _init_write_gz(self, compresslevel, mtime):
                                          self.zlib.DEF_MEM_LEVEL,
                                          0)
         if mtime is None:
-            mtime = int(time.time())
-        timestamp = struct.pack("<L", mtime)
+            mtime = time.time()
+        # gh-133998: substitute 0 for an out-of-range mtime and coerce to int,
+        # mirroring gzip (RFC 1952), so struct.pack cannot raise struct.error.
+        if not 0 <= mtime < 2**32:
+            mtime = 0
+        timestamp = struct.pack("<L", int(mtime))
         self.__write(b"\037\213\010\010" + timestamp + b"\002\377")
         if self.name.endswith(".gz"):
             self.name = self.name[:-3]
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 60666ff4cc100d..73e53d6cc3930f 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1983,6 +1983,44 @@ def test_create_with_mtime(self):
             fobj.read()
             self.assertEqual(fobj.mtime, 0)
 
+    def test_create_with_mtime_out_of_range(self):
+        # gh-133998: an mtime outside the gzip header's 32-bit range is
+        # stored as 0 rather than raising struct.error.
+        self.addCleanup(os_helper.unlink, tmpname)
+        for mtime in (-1, 2**32):
+            with self.subTest(mtime=mtime):
+                tarfile.open(tmpname, self.mode, mtime=mtime).close()
+                with self.open(tmpname, 'r') as fobj:
+                    fobj.read()
+                    self.assertEqual(fobj.mtime, 0)
+
+    def test_create_with_mtime_at_boundary(self):
+        # gh-133998: the largest in-range mtime is preserved, not clamped.
+        mtime = 2**32 - 1
+        tarfile.open(tmpname, self.mode, mtime=mtime).close()
+        with self.open(tmpname, 'r') as fobj:
+            fobj.read()
+            self.assertEqual(fobj.mtime, mtime)
+
+    def test_create_with_out_of_range_clock(self):
+        # gh-133998: an out-of-range system clock (mtime defaulting to
+        # time.time()) is stored as 0 rather than raising struct.error.
+        for clock in (-1, 2**32):
+            with self.subTest(clock=clock):
+                with unittest.mock.patch('time.time', return_value=float(clock)):
+                    tarfile.open(tmpname, self.mode).close()
+                with self.open(tmpname, 'r') as fobj:
+                    fobj.read()
+                    self.assertEqual(fobj.mtime, 0)
+                os_helper.unlink(tmpname)
+
+    def test_create_with_float_mtime(self):
+        # gh-133998: a float mtime is truncated like gzip, not rejected.
+        tarfile.open(tmpname, self.mode, mtime=123456789.9).close()
+        with self.open(tmpname, 'r') as fobj:
+            fobj.read()
+            self.assertEqual(fobj.mtime, 123456789)
+
     def test_create_without_mtime(self):
         before = int(time.time())
         tarfile.open(tmpname, self.mode).close()
diff --git a/Misc/NEWS.d/next/Library/2026-06-20-20-24-03.gh-issue-133998.nkqhMz.rst b/Misc/NEWS.d/next/Library/2026-06-20-20-24-03.gh-issue-133998.nkqhMz.rst
new file mode 100644
index 00000000000000..e7c03c662ec44f
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-06-20-20-24-03.gh-issue-133998.nkqhMz.rst
@@ -0,0 +1,4 @@
+Fix :func:`tarfile.open` in streaming write mode (``w|gz``) raising
+:exc:`struct.error` when given an *mtime* outside the range of the gzip
+header's 32-bit timestamp field.  Out-of-range values are now stored as ``0``,
+matching :mod:`gzip`.