The guard was on patrol in the southern Asir province when the mine exploded, the ministry said in a statement carried by the official SPA news agency.
Saudi Arabia heads an Arab military coalition which entered Yemen in March 2015 to prop up the government up against Iran-backed Huthi rebels.
Asir province is home to an airbase central to the coalition campaign.
The Huthis and their allies, troops loyal to former president Ali Abdullah Saleh, control much of northern Yemen and the Red Sea coast including the port of Hodeida.
The war in Yemen, one of the world's most impoverished countries, has killed more than 8,000 people and wounded a further 44,500 since Saudi Arabia and its allies joined the conflict.