The latest fatality brings to 11 the death toll in Saudi Arabia since Shiite Huthi rebels in Yemen began firing rockets and mortar rounds over the border last week.
Civil defence spokesman Ali al-Shahrani told Saudi news channel Al-Ekhbariya that a school and a residential area in Najran came under fire at 7:00 am local time.
He did not specify the source of the bombardment but said one person was killed. Three foreigners and a child were wounded.
The coalition has retaliated by declaring the whole of Saada province -- a Huthi stronghold on the border -- a military target and pounding it with air strikes and artillery fire.
Coalition spokesman Brigadier General Ahmed al-Assiri told AFP on Sunday that the retaliatory raids would continue right up to the proposed 11:00 pm local time Tuesday start-time for a five-day ceasefire, "if they continue to fire their rockets towards our cities, our population".