Saudi forces and the Houthis have been trading fire across the border since an Arab alliance began military operations against the Iranian-backed Shi’ite group in March to try to restore exiled President Abd-Rabbu Mansour Hadi to power.
Saudi state news agency SPA said the border guards were killed at a military post in Dhahran al-Janoub, along the border with Yemen, when projectiles fired from the Yemeni side struck.
Two of the soldiers died on the spot while five others were wounded and taken to a hospital, the agency said.
The Saudi-led coalition says it began their campaign heeding a call by Hadi after the Houthis started advancing south towards the port city of Aden, where the president was based.
The Houthis, who captured the Yemeni capital Sanaa last September, say they are fighting against Sunni Islamist militants using areas outside their control as staging grounds for attacks. They also accused officials in Hadi’s government of siphoning public funds.
On the ground, southern opposition fighters allied with Hadi said they had ambushed and killed six soldiers allied with the Houthis stationed in the south-eastern city of Zinjibar.
The World Health Organisation (WHO), which compiles figures on casualties in Yemen, said its latest figures show that 1,942 people had been killed between March 19 and May 22.
It said 7,870 people were injured in the same period.
Residents of the southern city of Aden said Houthi fighters at checkpoints outside the city had been preventing trucks carrying basic foodstuffs and qat – a narcotic leaf many Yemenis chew daily – from entering.
They said they believe the measures were a punishment after local fighters ejected the Houthis from the nearby city of Dhalea in the most serious setback for the group since March.
Houthi officials were not immediately available to comment on the reports.