diff --git a/builtin/show-ref.c b/builtin/show-ref.c
index 7aac525a87..6025ce223d 100644
--- a/builtin/show-ref.c
+++ b/builtin/show-ref.c
@@ -239,7 +239,7 @@ static int cmd_show_ref__exists(const char **refs)
 	if (refs_read_raw_ref(get_main_ref_store(the_repository), ref,
 			      &unused_oid, &unused_referent, &unused_type,
 			      &failure_errno)) {
-		if (failure_errno == ENOENT) {
+		if (failure_errno == ENOENT || failure_errno == EISDIR) {
 			error(_("reference does not exist"));
 			ret = 2;
 		} else {
diff --git a/t/t1403-show-ref.sh b/t/t1403-show-ref.sh
index b50ae6fcf1..a8055f7fe1 100755
--- a/t/t1403-show-ref.sh
+++ b/t/t1403-show-ref.sh
@@ -260,9 +260,9 @@ test_expect_success '--exists with non-commit object' '
 
 test_expect_success '--exists with directory fails with generic error' '
 	cat >expect <<-EOF &&
-	error: failed to look up reference: Is a directory
+	error: reference does not exist
 	EOF
-	test_expect_code 1 git show-ref --exists refs/heads 2>err &&
+	test_expect_code 2 git show-ref --exists refs/heads 2>err &&
 	test_cmp expect err
 '