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 Huthi 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.
Despite the coalition intervention, the Huthis 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.
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