Saudi authorities said on Saturday that the gun battle took place on Thursday after a border patrol spotted a vehicle attempting to cross Sharoora area in Najran province into Yemen.
The patrol came under fire when it tried to stop the vehicle, AFP reported, adding that the three men were arrested and are being questioned by authorities.
Meanwhile, Saudi border guards have killed three Yemeni citizens in a border area on Friday.
Local sources say Saudi guards surrounded the place where the victims were taking a rest and opened fire on them.
Following the incident, Yemeni media accused Sana’a government of acting weakly in dealing with the issue of Yemeni citizens trying to enter Saudi Arabia, saying that killing of Yemeni citizens entering the kingdom illegally has become a routine for Saudi border guards.