Three other assailants who died in the January 5 attack have already been identified as Saudis.
The fourth attacker was "killed during an exchange of fire by the suicide belt that he was wearing. His name is Salim Mohammed Faheed al-Shamry," the ministry said, quoted by the official Saudi Press Agency.
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The four were killed while "trying to infiltrate" the border, where guards confronted them, SPA said.
No group has claimed responsibility, but Saudi Arabia is among Arab countries taking part in US-led air strikes against the Islamic State jihadist group in Syria.
In details released earlier, the interior ministry said two attackers were shot dead and two detonated belts of explosives when the border patrol in the northern Arar region came under fire.
Among the three border guards killed was General Odah al-Balawi, a senior commander.