The trio opened fire after police ordered them to stop their vehicle at a roadblock near the capital’s Muntaza al-Salam (Park of Peace), one source said on Tuesday.
“The police patrol returned fire, killing the three suspects,” the source added.
Saudi authorities continue to battle al-Qaida-linked fighters who have carried out a wave of bombings and shootings in the kingdom.
More than 100 people have been killed and hundreds more wounded since May 2003.
The latest such attack, on the US consulate in Jedda, left five non-American employees dead on 6 December.
On Saturday, Saudi Crown Prince Abd Allah bin Abd al-Aziz called for vigilance from his countrymen in the face of those who “seek to destroy the country’s unity”, local media reported.