The attacker has been arrested, Saudi Interior Ministry spokesman General Mansour Turki said, adding that two people had also been wounded in the assault, which took place in the Aldair Bani Malik governorate in Jizan region.
Saudi newspaper Sabq posted a picture of emergency vehicles outside a four-storey building. Other local media described it as a personal dispute.
Saudi Arabia has seen several incidents of deadly violence in recent months. A suicide bombing and gun attack on Shi’ite Muslim worshippers killed at least four people in eastern Saudi Arabia in January.