diff --git a/kernel/cpu.c b/kernel/cpu.c
index 1a189da3bdac..303cb0591b4b 100644
--- a/kernel/cpu.c
+++ b/kernel/cpu.c
@@ -1523,11 +1523,14 @@ static int cpu_down_maps_locked(unsigned int cpu, enum cpuhp_state target)
 	/*
 	 * Ensure that the control task does not run on the to be offlined
 	 * CPU to prevent a deadlock against cfs_b->period_timer.
+	 * Also keep at least one housekeeping cpu onlined to avoid generating
+	 * an empty sched_domain span.
 	 */
-	cpu = cpumask_any_but(cpu_online_mask, cpu);
-	if (cpu >= nr_cpu_ids)
-		return -EBUSY;
-	return work_on_cpu(cpu, __cpu_down_maps_locked, &work);
+	for_each_cpu_and(cpu, cpu_online_mask, housekeeping_cpumask(HK_TYPE_DOMAIN)) {
+		if (cpu != work.cpu)
+			return work_on_cpu(cpu, __cpu_down_maps_locked, &work);
+	}
+	return -EBUSY;
 }
 
 static int cpu_down(unsigned int cpu, enum cpuhp_state target)