Another three members of the force were wounded in the explosion in Jizan province
A mine blast killed a Saudi border guard on Sunday on the kingdom's southern frontier with war-wracked Yemen, the interior ministry said.
Another three members of the force were wounded in the explosion in Jizan province, a spokesman cited by the official SPA news agency said.
Saudi Arabia has led a coalition battling Iran-backed Houthi rebels in its impoverished southern neighbour for the past two years.
At least 130 Saudi members of the security forces and civilians have been killed, mainly by rockets fired from Yemen, since the coalition intervened in support of President Abedrabbo Mansour Hadi in March 2015.
The Saudi-led coalition also comprises the Gulf countries of Bahrain, Kuwait, Qatar and the UAE along with Egypt, Jordan, Morocco and Sudan.
In two years, the rebels fired 47,847 rockets at Saudi territory, as well as "48 ballistic missiles, all of which were intercepted", coalition spokesman General Ahmed Assiri said in an interview broadcast Sunday by the television channel Al-Arabiya.
"We have an interest in keeping Yemen stable and the borders of the Saudi kingdom secure," Assiri said.
He also said Hadi's government controlled "80 to 85 percent of Yemeni territory" two years after the coalition intervened.
However, the Houthis still control the capital Sanaa and much of the northern highlands adjacent to the Saudi border.
The United Nations says that more than 7,700 people have been killed over the past two years in Yemen, which also faces a serious risk of famine this year.
UN attempts at mediation and seven ceasefire accords have come to nothing.