The Border Guards at a post in the kingdom's southwestern Asir region came "under fire from a mountainous interior zone," the interior ministry said in a statement on the official Saudi Press Agency.
Saudi Arabia has 150,000 troops and 100 warplanes assigned to the Yemen operation, according to a Saudi adviser, but says it has no plan for now to send ground forces into the neighbouring country.
Last Friday a US defence official said two Saudi pilots who ejected from their F-15 jet off Yemen's coast had been rescued.
In Jazan region, a border district adjacent to Asir, the closure of 49 schools will be extended for a week beginning Sunday as a "precautionary measure" because of their location near the Yemeni frontier, the Saudi Press Agency said, citing an education official.