diff --git a/builtin/index-pack.c b/builtin/index-pack.c
index fd968d673d22d8..763b01372aade4 100644
--- a/builtin/index-pack.c
+++ b/builtin/index-pack.c
@@ -1868,6 +1868,15 @@ int cmd_index_pack(int argc, const char **argv, const char *prefix)
 	if (!index_name && pack_name)
 		index_name = derive_filename(pack_name, "pack", "idx", &index_name_buf);
 
+	/*
+	 * Packfiles and indices do not carry enough information to be able to
+	 * identify their object hash. So when we are neither in a repository
+	 * nor has the user told us which object hash to use we have no other
+	 * choice but to guess the object hash.
+	 */
+	if (!the_repository->hash_algo)
+		repo_set_hash_algo(the_repository, GIT_HASH_SHA1);
+
 	opts.flags &= ~(WRITE_REV | WRITE_REV_VERIFY);
 	if (rev_index) {
 		opts.flags |= verify ? WRITE_REV_VERIFY : WRITE_REV;
diff --git a/t/t5300-pack-object.sh b/t/t5300-pack-object.sh
index 4ad023c846d06a..3b9dae331a5ea9 100755
--- a/t/t5300-pack-object.sh
+++ b/t/t5300-pack-object.sh
@@ -635,4 +635,43 @@ test_expect_success 'negative window clamps to 0' '
 	check_deltas stderr = 0
 '
 
+for hash in sha1 sha256
+do
+	test_expect_success "verify-pack with $hash packfile" '
+		test_when_finished "rm -rf repo" &&
+		git init --object-format=$hash repo &&
+		test_commit -C repo initial &&
+		git -C repo repack -ad &&
+		git -C repo verify-pack "$(pwd)"/repo/.git/objects/pack/*.idx &&
+		if test $hash = sha1
+		then
+			nongit git verify-pack "$(pwd)"/repo/.git/objects/pack/*.idx
+		else
+			# We have no way to identify the hash used by packfiles
+			# or indices, so we always fall back to SHA1.
+			nongit test_must_fail git verify-pack "$(pwd)"/repo/.git/objects/pack/*.idx &&
+			# But with an explicit object format we should succeed.
+			nongit git verify-pack --object-format=$hash "$(pwd)"/repo/.git/objects/pack/*.idx
+		fi
+	'
+
+	test_expect_success "index-pack outside of a $hash repository" '
+		test_when_finished "rm -rf repo" &&
+		git init --object-format=$hash repo &&
+		test_commit -C repo initial &&
+		git -C repo repack -ad &&
+		git -C repo index-pack --verify "$(pwd)"/repo/.git/objects/pack/*.pack &&
+		if test $hash = sha1
+		then
+			nongit git index-pack --verify "$(pwd)"/repo/.git/objects/pack/*.pack
+		else
+			# We have no way to identify the hash used by packfiles
+			# or indices, so we always fall back to SHA1.
+			nongit test_must_fail git index-pack --verify "$(pwd)"/repo/.git/objects/pack/*.pack 2>err &&
+			# But with an explicit object format we should succeed.
+			nongit git index-pack --object-format=$hash --verify "$(pwd)"/repo/.git/objects/pack/*.pack
+		fi
+	'
+done
+
 test_done