diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 55e4a4e0c9a29c..7660c1dbc44ba4 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -520,7 +520,9 @@ def seek(self, pos=0):
         if pos - self.pos >= 0:
             blocks, remainder = divmod(pos - self.pos, self.bufsize)
             for i in range(blocks):
-                self.read(self.bufsize)
+                data = self.read(self.bufsize)
+                if not data:
+                    break
             self.read(remainder)
         else:
             raise StreamError("seeking backwards is not allowed")
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 4be207e8cbf4e6..04c4e990a69d73 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -4802,6 +4802,22 @@ def valueerror_filter(tarinfo, path):
         with self.check_context(arc.open(errorlevel='boo!'), filtererror_filter):
             self.expect_exception(TypeError)  # errorlevel is not int
 
+    @support.subTests('format', [tarfile.GNU_FORMAT, tarfile.PAX_FORMAT])
+    def test_getmembers_big_size(self, format):
+        # gh-151981: A loop in seek() for streaming files tried to read the
+        # declared number of blocks even at EOF
+        tinfo = tarfile.TarInfo("huge-file")
+        tinfo.size = 1 << 64
+        bio = io.BytesIO()
+        # Write header without data
+        bio.write(tinfo.tobuf(format))
+
+        # Reset & try to get contents
+        bio.seek(0)
+        with tarfile.open(fileobj=bio, mode="r|") as tar:
+            with self.assertRaises(tarfile.ReadError):
+                tar.getmembers()
+
 
 class OverwriteTests(archiver_tests.OverwriteTests, unittest.TestCase):
     testdir = os.path.join(TEMPDIR, "testoverwrite")
diff --git a/Misc/NEWS.d/next/Security/2026-06-23-13-28-16.gh-issue-151981.xBHEcU.rst b/Misc/NEWS.d/next/Security/2026-06-23-13-28-16.gh-issue-151981.xBHEcU.rst
new file mode 100644
index 00000000000000..2123ab8e081b1d
--- /dev/null
+++ b/Misc/NEWS.d/next/Security/2026-06-23-13-28-16.gh-issue-151981.xBHEcU.rst
@@ -0,0 +1,2 @@
+In :mod:`tarfile`, seeking a stream now stops when end of the stream is
+reached.