diff --git a/builtin/repack.c b/builtin/repack.c
index 63585ad046..a591a4ddd6 100644
--- a/builtin/repack.c
+++ b/builtin/repack.c
@@ -570,6 +570,17 @@ static void midx_included_packs(struct string_list *include,
 		for (i = geometry->split; i < geometry->pack_nr; i++) {
 			struct packed_git *p = geometry->pack[i];
 
+			/*
+			 * The multi-pack index never refers to packfiles part
+			 * of an alternate object database, so we skip these.
+			 * While git-multi-pack-index(1) would silently ignore
+			 * them anyway, this allows us to skip executing the
+			 * command completely when we have only non-local
+			 * packfiles.
+			 */
+			if (!p->pack_local)
+				continue;
+
 			strbuf_addstr(&buf, pack_basename(p));
 			strbuf_strip_suffix(&buf, ".pack");
 			strbuf_addstr(&buf, ".idx");
diff --git a/t/t7703-repack-geometric.sh b/t/t7703-repack-geometric.sh
index 4abc7d4c55..9dd002437f 100755
--- a/t/t7703-repack-geometric.sh
+++ b/t/t7703-repack-geometric.sh
@@ -313,4 +313,27 @@ test_expect_success '--geometric --write-midx with packfiles in main and alterna
 	test_cmp expect actual
 '
 
+test_expect_success '--geometric --with-midx with no local objects' '
+	test_when_finished "rm -fr shared member" &&
+
+	# Create a repository with a single packfile that acts as alternate
+	# object database.
+	git init shared &&
+	test_commit -C shared "shared-objects" &&
+	git -C shared repack -ad &&
+
+	# Create a second repository linked to the first one and perform a
+	# geometric repack on it.
+	git clone --shared shared member &&
+	git -C member repack --geometric 2 --write-midx 2>err &&
+	test_must_be_empty err &&
+
+	# Assert that we wrote neither a new packfile nor a multi-pack-index.
+	# We should not have a packfile because the single packfile in the
+	# alternate object database does not invalidate the geometric sequence.
+	# And we should not have a multi-pack-index because these only index
+	# local packfiles, and there are none.
+	test_dir_is_empty member/$packdir
+'
+
 test_done