diff --git a/builtin/fetch.c b/builtin/fetch.c
index e45185cf9c..f1fe73a3e0 100644
--- a/builtin/fetch.c
+++ b/builtin/fetch.c
@@ -1643,6 +1643,16 @@ static int do_fetch(struct transport *transport,
 			}
 		}
 		if (source_ref) {
+			if (!branch) {
+				const char *shortname = source_ref->name;
+				skip_prefix(shortname, "refs/heads/", &shortname);
+
+				warning(_("could not set upstream of HEAD to '%s' from '%s' when "
+					  "it does not point to any branch."),
+					shortname, transport->remote->name);
+				goto skip;
+			}
+
 			if (!strcmp(source_ref->name, "HEAD") ||
 			    starts_with(source_ref->name, "refs/heads/"))
 				install_branch_config(0,
diff --git a/t/t5553-set-upstream.sh b/t/t5553-set-upstream.sh
index 9c12c0f8c3..48050162c2 100755
--- a/t/t5553-set-upstream.sh
+++ b/t/t5553-set-upstream.sh
@@ -91,6 +91,17 @@ test_expect_success 'fetch --set-upstream with valid URL sets upstream to URL' '
 	check_config_missing other2
 '
 
+test_expect_success 'fetch --set-upstream with a detached HEAD' '
+	git checkout HEAD^0 &&
+	test_when_finished "git checkout -" &&
+	cat >expect <<-\EOF &&
+	warning: could not set upstream of HEAD to '"'"'main'"'"' from '"'"'upstream'"'"' when it does not point to any branch.
+	EOF
+	git fetch --set-upstream upstream main 2>actual.raw &&
+	grep ^warning: actual.raw >actual &&
+	test_cmp expect actual
+'
+
 # tests for pull --set-upstream
 
 test_expect_success 'setup bare parent pull' '
@@ -178,4 +189,15 @@ test_expect_success 'pull --set-upstream with valid URL and branch sets branch'
 	check_config_missing other2
 '
 
+test_expect_success 'pull --set-upstream with a detached HEAD' '
+	git checkout HEAD^0 &&
+	test_when_finished "git checkout -" &&
+	cat >expect <<-\EOF &&
+	warning: could not set upstream of HEAD to '"'"'main'"'"' from '"'"'upstream'"'"' when it does not point to any branch.
+	EOF
+	git pull --no-rebase --set-upstream upstream main 2>actual.raw &&
+	grep ^warning: actual.raw >actual &&
+	test_cmp expect actual
+'
+
 test_done