Following a shootout, police and security forces cordoned off a neighborhood in western Riyadh in a search for other suspects, the officials said on condition of anonymity.
None of the three were identified by name and it was not known if they were on the kingdom's list of 26 most wanted militants.
Eyewitnesses said several ambulances were seen heading to the site of the shootout while military helicopters hovered over the area.
The Gulf-based Al-Arabiya television network reported that the 10-15 minute shootout occurred at a gas station when police stopped a car for routine check. A reporter for the network said the passengers opened fire at the police officers as they approached the car.
A fire broke out at the station but there were no reports of other casualties, the reporter said.
Saudi Arabia has launched a crackdown on terrorism that has resulted in the killings and arrests of dozens of militants. The last raid on suspected militants came Nov. 16, when police arrested five suspects after a shootout that killed a Saudi policeman in al-Qassim, 220 miles northwest of Riyadh, the capital. Police seized automatic rifles, pipe bombs and more than $10,000.
But despite the government's efforts, gunmen still managed to attack the U.S. Consulate in the port city of Jiddah on Dec. 6. Nine people were killed in the attack, including four of the attackers when security forces stormed the compound.