The state SPA news agency said the fighter was killed in a shootout on Friday after a car chase through residential neighbourhoods of the town.
"It transpired that he was wanted in security-related matters ... another participant in the incident was identified and arrested," the official said.
Interior Ministry spokesman Mansur al-Turki said a security officer was killed the previous night when his patrol came under fire in the same town, 340km northwest of Riyadh.
Saudi security forces have repeatedly clashed with anti-government fighters blamed for a wave of violence in the desert kingdom since May 2003.
On Monday, security forces killed a man and wounded three others in the eastern al-Ahsaa region while they drove their car towards a checkpoint with its lights switched off.
The Interior Ministry later clarified that the men were not "terror-suspects" and the shootout was a mistake.
Some 90 people have been killed and hundreds wounded in the spate of bombings and shootings in Saudi Arabia - much of it directed at Westerners - over the past 16 months.