The incident took place on Sunday afternoon when a man sped away in his car after police tried to carry out a check on the vehicle in the eastern al-Nassim neighbourhood.
As the man tried to escape, his companion opened fire at the police patrol, the police chief said in a statement carried by the official SPA news agency.
The police chased the vehicle and exchanged fire with the two men, whose vehicle broke down.
"The driver and his companion stopped in a busy area, hijacked the car of a citizen at gunpoint and fled, but there were no casualties," the police chief said.
"A number of suspects were arrested and the incident is still being followed up," the unnamed police chief said without giving details.
A police source later corroborated the chain of events, but made no mention of arrests.
Saudi security forces have repeatedly clashed with suspected "militants" in the past months, as they hunt for persons associated with al-Qaida network.
Hundreds of suspects have been rounded up since last May's triple bombings of residential compounds in Riyadh which killed 35 people, including eight Americans.
A car bomb went off at another expatriate housing complex in the Saudi capital in November, killing 17 people, mostly Arabs.