Huthi rebels backed by renegade troops loyal to former president Ali Abdullah Saleh tried to infiltrate the borders in the southern Najran area, the coalition fighting the rebels said in a statement carried by the SPA state news agency.
“An officer and six soldiers of the Saudi armed forces fell martyrs,” said the statement, adding that Saudi warplanes had repelled the attackers.
It claimed that dozens of the rebels were killed.
On Monday, five Saudi border guards were killed in similar border clashes in the Najran area.
Southern Saudi Arabia, especially border areas with Yemen, have come under sporadic attack since Riyadh took the lead in March 2015 in an Arab military coalition battling Huthi rebels who control northern Yemen.
Around 100 members of the Saudi forces and civilians have been killed in skirmishes, by artillery fire or landmines inside the kingdom’s borders since the coalition launched its campaign.
More than 6,400 Yemenis, most of them civilians, have been killed since last March, and the fighting has driven 2.8 Yemenis from their homes.
Kuwait has hosted Yemen peace talks since April but the negotiations have failed to make any progress.
The UN special envoy for Yemen made a last-ditch bid Saturday to salvage the talks by proposing to extend them for one week, after the government delegation said it planned to quit the Kuwait discussions.