According to the SPA news agency on Thursday, the announcement came as the king visited front-line troops in the southern province of Jizan, where Saudi forces have been battling Yemeni rebels for over four weeks.
Thousands of nationals who live along the mountainous border have been relocated to tent camps inland as the Saudis aim to set up 10 kilometre buffer zones on either side of the border.
The order to build new housing appears to confirm reports that Riyadh intends the buffer to be permanent, at least on the Saudi side.
It is the king's first visit to the area since the army began shelling the rugged border with northwest Yemen in early November.
The Saudi military is undertaking its largest mobilisation since the 1990-91 Gulf War following a minor border incursion by the Huthis, deploying fighter bombers, heavy artillery, special forces and naval vessels against the rebels.
The Saudis say they are acting to prevent the Huthis and other threats from crossing into Saudi territory, after a band killed a Saudi border guard and temporarily occupied two Jizan villages on November 3.
Analysts say the Saudis are also closely assisting Yemen's government in its effort to crush the rebellion.
Saudi-owned regional daily Asharq al-Awsat reported on Wednesday that bombers and artillery continued to hit Huthi positions this week and that ground troops using armoured vehicles were patrolling the region to search for rebels.
Ten Saudi soldiers have died in the conflict, according to an unofficial toll.