Four other Saudis who also had "criminal records and have taken part in terror acts" were arrested following the clash yesterday morning, the ministry said in a statement carried by state news agency SPA.
It said security forces were storming a farm north of the town of Awamiya "used by terrorists for plotting and preparation of terror attacks" when they came under fire from a nearby farm.
Police found ammunition and materials for making explosives in both farms after the clash in which security forces "killed those who opened fire", it said.
It was the home of Nimr al-Nimr, a Shiite cleric put to death in January last year for "terrorism". His execution prompted Iranian protesters to torch Saudi diplomatic missions, leading Riyadh to sever ties with Tehran.
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Nimr was a driving force behind protests by Shiite residents that began in 2011 and developed into a call for equality in the Sunni-majority kingdom.
A teenage suspect died from wounds earlier this month when police retaliated after coming under fire while looking for suspects hiding among abandoned homes in Awamiya.