Quoted by Al-Ekhbariya state television, the agency the five other wounded in the city of Najran were all Yemeni citizens.
Video footage posted on social networks showed two blazing buildings in the city centre.
Cross-border attacks into Saudi Arabia have increased since a Saudi-led Arab coalition this month stepped up air strikes on insurgent targets inside Yemen in an attempt to shore up the beleaguered government.
Saturday's attack was the third this week.
On Friday, five foreign residents of Najran were wounded in a rocket strike just west of the city.
Seven civilians were killed on Tuesday when the city centre was shelled, with three victims said to be expats.
Meanwhile, the rebel-controlled Saba news agency reported a wave of coalition raids inside Yemen on Saturday, including one that killed three civilians near the Huthi-held capital Sanaa.
Despite the reported attacks, Saba said that "thousands" of people demonstrated in Sanaa in support of the rebels and their allies, forces loyal to ousted president Ali Abdullah Saleh.