Rocket fire by Yemeni rebels killed a policeman and wounded a civilian on the Saudi side of the border, the civil defence department said late on Wednesday.
They were the latest casualties inside the kingdom since Saudi Arabia began leading an Arab military coalition that intervened in its southern neighbour to support President Abedrabbo Mansour Hadi in March 2015.
At least 128 people have died in southern Saudi Arabia since the intervention began -- some in border skirmishes, others in rocket fire.
Video footage circulating on social media showed shattered glass and a trail of blood at the entrance to a court building in Dhahran South that its posters said was the aftermath of the Wednesday rocket strike.
The building's front wall was pockmarked from shrapnel. A guard house appeared to have taken the brunt of the strike, and a policeman sat slumped and bloodied in his chair, apparently dead.
The death toll has been far higher on the other side of the border.
More than 7,400 people have been killed in Yemen since the Saudi-led intervention began, including around 1,400 children, according to World Health Organization figures.
The UN humanitarian coordinator for Yemen, Jamie McGoldrick, said on Tuesday that the death toll was closer to 10,000.