diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index a4f9ce3311f6dad..e995f9d5c867211 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1494,6 +1494,8 @@ def _proc_sparse(self, tarfile):
         # Collect sparse structures from extended header blocks.
         while isextended:
             buf = tarfile.fileobj.read(BLOCKSIZE)
+            if len(buf) < BLOCKSIZE:
+                raise ReadError("unexpected end of data")
             pos = 0
             for i in range(21):
                 try:
diff --git a/Misc/NEWS.d/next/Library/2026-09-25-17-42-56.gh-issue-158181.v7PCZg.rst b/Misc/NEWS.d/next/Library/2026-09-25-17-42-56.gh-issue-158181.v7PCZg.rst
new file mode 100644
index 000000000000000..20d5424cf36a885
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-09-25-17-42-56.gh-issue-158181.v7PCZg.rst
@@ -0,0 +1,3 @@
+Fix :exc:`IndexError` instead of :exc:`tarfile.ReadError` when
+:mod:`tarfile` reads a truncated GNU sparse member whose extended header
+block is missing or short.