diff --git a/builtin/rebase.c b/builtin/rebase.c
index b29ad2b65e..27fde7bf28 100644
--- a/builtin/rebase.c
+++ b/builtin/rebase.c
@@ -829,6 +829,8 @@ static int checkout_up_to_date(struct rebase_options *options)
 	ropts.oid = &options->orig_head;
 	ropts.branch = options->head_name;
 	ropts.flags = RESET_HEAD_RUN_POST_CHECKOUT_HOOK;
+	if (!ropts.branch)
+		ropts.flags |=  RESET_HEAD_DETACH;
 	ropts.head_msg = buf.buf;
 	if (reset_head(the_repository, &ropts) < 0)
 		ret = error(_("could not switch to %s"), options->switch_to);
diff --git a/t/t3400-rebase.sh b/t/t3400-rebase.sh
index 71b1735e1d..d5a8ee39fc 100755
--- a/t/t3400-rebase.sh
+++ b/t/t3400-rebase.sh
@@ -18,10 +18,7 @@ GIT_AUTHOR_EMAIL=bogus@email@address
 export GIT_AUTHOR_NAME GIT_AUTHOR_EMAIL
 
 test_expect_success 'prepare repository with topic branches' '
-	git config core.logAllRefUpdates true &&
-	echo First >A &&
-	git update-index --add A &&
-	git commit -m "Add A." &&
+	test_commit "Add A." A First First &&
 	git checkout -b force-3way &&
 	echo Dummy >Y &&
 	git update-index --add Y &&
@@ -32,9 +29,7 @@ test_expect_success 'prepare repository with topic branches' '
 	git mv A D/A &&
 	git commit -m "Move A." &&
 	git checkout -b my-topic-branch main &&
-	echo Second >B &&
-	git update-index --add B &&
-	git commit -m "Add B." &&
+	test_commit "Add B." B Second Second &&
 	git checkout -f main &&
 	echo Third >>A &&
 	git update-index A &&
@@ -399,6 +394,15 @@ test_expect_success 'switch to branch not checked out' '
 	git rebase main other
 '
 
+test_expect_success 'switch to non-branch detaches HEAD' '
+	git checkout main &&
+	old_main=$(git rev-parse HEAD) &&
+	git rebase First Second^0 &&
+	test_cmp_rev HEAD Second &&
+	test_cmp_rev main $old_main &&
+	test_must_fail git symbolic-ref HEAD
+'
+
 test_expect_success 'refuse to switch to branch checked out elsewhere' '
 	git checkout main &&
 	git worktree add wt &&