The shootout late on Tuesday erupted when security forces stormed a house in the capital's King Fahd neighbourhood.
The official SPA news agency said that security forces detained the wife and three children of Salih al-Awfi, believed to be the leader of al-Qaida in the kingdom, in the same operation.
An explosion was heard and heavy gunfire continued for more than an hour after the team cordoned off the site. Armoured vehicles had been sent in.
One witness said he saw police cars chasing armed men in a small Toyota truck from the Musrassalat quarter to the King Fahd neighbourhood nearby.
The incident took place ahead of the expiry later this week of a royal amnesty offered to anti-government fighters.
The authorities have said the amnesty will not be extended and those who opted not to take advantage of it have been threatened with a harsh crackdown.