The agency quoted an unidentified Interior Ministry security official who said police were investigating the shooting in al-Zahra district of the city early Sunday.
The official gave no further details and the motive of the attack was not immediately clear.
There was no indication of whether the shooting was the latest attack in a campaign launched by anti-government forces believed to be allied with the al-Qaida network.
The oil-rich kingdom has witnessed an apparent campaign to drive Westerners out and hurt the economy and oil industry.
More than 100 policemen and civilians, many of them foreigners, have been killed in a wave of shootings and bombings.