The officials, speaking on condition of anonymity, said police patrolling the affluent suburb of Roda, east of Riyadh, fired at a car that refused their order to stop.
The officials told The Associated Press that police fired at two "wanted militants" who were in the car, killing one and wounding a second.
Eyewitnesses said the militants fired first. Officials said the ensuing gun battle injured three other people, but it was not immediately clear if they were police or bystanders.
Police have cornered the wounded militant inside a villa in the area, which has been cordoned off and surrounded by security forces and several armored vehicles. Ambulances have arrived.
It was not immediately clear what the militants were wanted for, but Saudi Arabia, the birthplace of al Qaeda leader Osama bin Laden, has been on high alert since terrorists carried out several attacks aimed at destabilizing the U.S.-allied Gulf state and home to Islam's two holiest shrines.
Saudi authorities released a list of 26 most wanted terrorists after a series of bombings in Riyadh on May 12, 2003, that killed 26 people. On Nov. 8, another suicide attack on a Riyadh housing compound killed 17 people.
Three of Saudi's most wanted list are dead and hundreds of suspected extremists have been rounded up in raids to seize weapons and Islamic militants.