Colonel Hassan Ghasoum Ageeli and a deputy sergeant died late Friday in the Jazan district, and four other guards were lightly wounded, the ministry said in a statement.
Ageeli is one of the most senior Saudi officers killed since March when the kingdom formed an Arab coalition to fight Houthis in Yemen, AFP reported.
The landmine blast damaged vehicles patrolling the border district, the ministry said.
After backup arrived, "they were subject to heavy shooting from several locations inside the Yemeni border," sparking a firefight, it said.
Riyadh launched air strikes against the Houthis six months ago to restore power to fugitive former Yemeni President Abedrabbo Mansour Hadi.
Saudi Arabia feared the Houthis would take over all of Yemen and move its neighbour into the orbit of the regional rival Iran.
In June, a Saudi lieutenant colonel died in a landmine blast in Jazan, while a general in August became the highest-ranked Saudi fatality when he was killed in cross-border fire.