Five of the gunmen were killed in the confrontation with security forces, including two who blew themselves up, while a sixth was wounded and arrested.
The ministry named the culprits, saying they were "all wanted Saudis" who were identified through DNA tests and that four of the gunmen had done time in jail, according to a statement carried by SPA state news agency.
The ministry had said that the militants attacked the Wadia border post in the south of the kingdom on Friday, an operation claimed by al Qaeda in the Arabian Peninsula.
The crossing is in Yemen's southeastern province of Hadramawt, whose rugged terrain provides hideouts for AQAP militants.
AQAP, born in 2009 of a fusion of the Saudi and Yemeni branches of al Qaeda, is considered by Washington to be the network's most dangerous affiliate.
To counter illegal crossings and arms smuggling, Saudi Arabia is building a three-metre high fence along its southern frontier.
Taking advantage of a collapse of central authority during a 2011 uprising that forced Yemen's veteran strongman Ali Abdullah Saleh from power, al Qaeda seized swathes of the country's south and east.
Saudi Arabia launched a massive crackdown on al Qaeda following a spate of deadly attacks in the kingdom from 2003-2006.
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Why did the Saudi not revoke their nationalities.... like they did another son of a soil OBL? a scheme best known to Saudi Government.