An Interior Ministry spokesman later said four Iraqi car thieves had been arrested after the firefight.
"The Iraqis slipped into the country to try to steal cars and smuggle them out. Police officers arrested them after an exchange of gunfire," the spokesman said, adding one of the Iraqis was injured and taken to hospital.
The spokesman said such incidents were not infrequent but an investigation would attempt to determine if the clash was connected to a wave of al-Qaida violence that has swept the kingdom in the past two years.
The world's top oil producer has been battling a wave of attacks over the past two years. Insurgents are attempting to overthrow the pro-Washington ruling royal family and drive Westerners out of the kingdom.
At least 91 foreign nationals and Saudi civilians have been killed in the attacks.
Saudi forces thwarted imminent attacks last week by rounding up 41 suspected fighters in a series of raids across the kingdom, the Interior Ministry said on Friday.
The arrests came less than 10 days after the killing of al-Qaida's leader in the country, Saleh al-Awfi. Thirteen people were arrested on on 18 August, the same day al-Awfi was killed.