The exchange of fire between border guards and gunmen took place on Friday near the Wadia border crossing that links Saudi Arabia with Yemen ' s Hadhramaut province.
The Saudi Arabian border guard was shot dead when gunmen opened fire on his patrol.
The ensuing clashes between the two sides left three militants dead.
“A security patrol came under fire from assailants… which required responding to the source of fire similarly, ” Saudi Interior Ministry spokesman Mansour al - Turki told the official Saudi Press Agency(SPA).
“The exchange of fire resulted in(the) killing of three of the attackers, ” one was wounded and another arrested, Turki stated.
A Yemeni soldier was also killed by the gunmen on the other side of the border.
Border security has deteriorated in the region in recent years.
Yemeni security forces frequently come under attack by gunmen especially in the southern and eastern parts of the country.
On August 31,2013, Yemeni Prime Minister Mohammed Salim Basindawa escaped an assassination attempt by unknown gunmen, who opened fire on his convoy in the capital Sana’a.
In December 2012, two armed men killed Lieutenant Colonel Mutei Baqatyan, a member of the country’s state security, in an attack in the southern city of Mukalla.
Yemeni Defense Minister Mohammed Nasser Ahmed was also seriously injured and 12 people were killed in a car bomb attack that targeted his motorcade in the heart of the capital in September 2012.