Agency spokesman Yehia al-Kahtani said a shell struck a house in Jizan city near border with Yemen, injuring a man and his sister, the official SPA news agency reported.
The cross-border fire was the first on Saudi territory from Yemen in more than one month.
There was no claim of responsibility for the fire, but the Saudi-Yemeni borderline has been witnessing clashes between Saudi troops and Yemeni’s Shia Houthi rebels, which Riyadh accuses of being a proxy force for regional rival Iran.
Yemen has been wracked by chaos since late 2014, when the Houthis and their allies overran capital Sanaa and other parts of the country.
The conflict escalated last year when Saudi Arabia and its Arab allies launched a major air campaign aimed at reversing Houthi gains and supporting Yemen’s Saudi-backed government.
Two rounds of UN-backed peace talks have failed to resolve the raging conflict, in which thousands of Yemenis are believed to have been killed and an estimated 2.5 million forced to flee their homes.