Earlier, the Houthis said they carried out drone attacks on Jizan and Abha Saudi airports.
Iran-aligned Houthis, who are fighting in neighboring Yemen, have repeatedly launched attacks against targets in Saudi Arabia, which is leading a coalition battling them.
A Houthi drone attack on Abha civilian airport wounded nine civilians on Tuesday.
The rebels in neighboring Yemen -- who have faced persistent coalition bombing since March 2015 which has exacted a heavy civilian death toll -- have stepped up missile and drone attacks across the border in recent weeks.
On June 12, a rebel missile attack on Abha airport wounded 26 civilians, drawing promises of "stern action" from the coalition.
And on June 23, another rebel attack on Abha airport killed a Syrian national and wounded 21 other civilians, according to the coalition.
The coalition intervened in support of the Yemeni government in 2015 when President Abedrabbo Mansour Hadi fled into Saudi exile as the rebels closed in on his last remaining territory in and around the second city Aden.
Since then, the conflict has killed tens of thousands of people, many of them civilians, relief agencies say.
The fighting has triggered what the United Nations describes as the world's worst humanitarian crisis, with millions of people displaced and in need of aid.