diff --git a/builtin/repack.c b/builtin/repack.c
index 5768aeb1f3..e2abcea2ee 100644
--- a/builtin/repack.c
+++ b/builtin/repack.c
@@ -887,6 +887,18 @@ int cmd_repack(int argc, const char **argv, const char *prefix)
 	if (write_bitmaps && !(pack_everything & ALL_INTO_ONE) && !write_midx)
 		die(_(incremental_bitmap_conflict_error));
 
+	if (write_bitmaps && po_args.local && has_alt_odb(the_repository)) {
+		/*
+		 * When asked to do a local repack, but we have
+		 * packfiles that are inherited from an alternate, then
+		 * we cannot guarantee that the multi-pack-index would
+		 * have full coverage of all objects. We thus disable
+		 * writing bitmaps in that case.
+		 */
+		warning(_("disabling bitmap writing, as some objects are not being packed"));
+		write_bitmaps = 0;
+	}
+
 	if (write_midx && write_bitmaps) {
 		struct strbuf path = STRBUF_INIT;
 
diff --git a/object-file.c b/object-file.c
index 8fab8dbe80..3ad11c683b 100644
--- a/object-file.c
+++ b/object-file.c
@@ -946,6 +946,12 @@ void prepare_alt_odb(struct repository *r)
 	r->objects->loaded_alternates = 1;
 }
 
+int has_alt_odb(struct repository *r)
+{
+	prepare_alt_odb(r);
+	return !!r->objects->odb->next;
+}
+
 /* Returns 1 if we have successfully freshened the file, 0 otherwise. */
 static int freshen_file(const char *fn)
 {
diff --git a/object-store.h b/object-store.h
index 82201ec3e7..574f16140f 100644
--- a/object-store.h
+++ b/object-store.h
@@ -56,6 +56,7 @@ KHASH_INIT(odb_path_map, const char * /* key: odb_path */,
 	struct object_directory *, 1, fspathhash, fspatheq)
 
 void prepare_alt_odb(struct repository *r);
+int has_alt_odb(struct repository *r);
 char *compute_alternate_path(const char *path, struct strbuf *err);
 struct object_directory *find_odb(struct repository *r, const char *obj_dir);
 typedef int alt_odb_fn(struct object_directory *, void *);
diff --git a/t/t7700-repack.sh b/t/t7700-repack.sh
index 4aabe98139..93c5763e7d 100755
--- a/t/t7700-repack.sh
+++ b/t/t7700-repack.sh
@@ -106,6 +106,23 @@ test_expect_success SYMLINKS '--local keeps packs when alternate is objectdir '
 	test_cmp expect actual
 '
 
+test_expect_success '--local disables writing bitmaps when connected to alternate ODB' '
+	test_when_finished "rm -rf shared member" &&
+
+	git init shared &&
+	git clone --shared shared member &&
+	(
+		cd member &&
+		test_commit "object" &&
+		git repack -Adl --write-bitmap-index 2>err &&
+		cat >expect <<-EOF &&
+		warning: disabling bitmap writing, as some objects are not being packed
+		EOF
+		test_cmp expect err &&
+		test ! -f .git/objects/pack-*.bitmap
+	)
+'
+
 test_expect_success 'packed obs in alt ODB are repacked even when local repo is packless' '
 	mkdir alt_objects/pack &&
 	mv .git/objects/pack/* alt_objects/pack &&
diff --git a/t/t7703-repack-geometric.sh b/t/t7703-repack-geometric.sh
index c440956ad5..33d7977fca 100755
--- a/t/t7703-repack-geometric.sh
+++ b/t/t7703-repack-geometric.sh
@@ -419,4 +419,31 @@ test_expect_success '--geometric -l with non-intact geometric sequence across OD
 	test_cmp expected-objects actual-objects.sorted
 '
 
+test_expect_success '--geometric -l disables writing bitmaps with non-local packfiles' '
+	test_when_finished "rm -fr shared member" &&
+
+	git init shared &&
+	test_commit_bulk -C shared --start=1 1 &&
+
+	git clone --shared shared member &&
+	test_commit_bulk -C member --start=2 1 &&
+
+	# When performing a geometric repack with `-l` while connecting to an
+	# alternate object database that has a packfile we do not have full
+	# coverage of objects. As a result, we expect that writing the bitmap
+	# will be disabled.
+	git -C member repack -l --geometric=2 --write-midx --write-bitmap-index 2>err &&
+	cat >expect <<-EOF &&
+	warning: disabling bitmap writing, as some objects are not being packed
+	EOF
+	test_cmp expect err &&
+	test ! -f member/.git/objects/pack/multi-pack-index-*.bitmap &&
+
+	# On the other hand, when we repack without `-l`, we should see that
+	# the bitmap gets created.
+	git -C member repack --geometric=2 --write-midx --write-bitmap-index 2>err &&
+	test_must_be_empty err &&
+	test -f member/.git/objects/pack/multi-pack-index-*.bitmap
+'
+
 test_done
