Eight policemen were slightly wounded in the clash in the capital’s Suwaidi residential area, reported the official Saudi Press Agency on Thursday, quoting an interior ministry official.
The official said an unspecified number of suspects had escaped, but gave no further details.
And in Makka, two so-called “terrorists” blew themselves up as security forces searched for suspected armed dissidents, according to security sources.
On Tuesday the interior ministry said police had foiled a plot to attack Muslim pilgrims in the holy city of Makka and, during a raid, had killed two suspects believed to be linked to the al-Qaida network.
But Saudi dissident Dr Saad al-Faqih said six suspects and five security officers were killed in the shootout.
The Makka clashes came more than a week after the United States and Britain warned of a threat of attacks on Western targets in the kingdom during the Muslim holy month of Ramadan, which began in late October.
Five suspects allegedly linked to the plot were arrested.
Saudi Arabia has launched an intensive crackdown on those suspected of plotting to carry out attacks against Western targets and Riyadh itself, after a triple bombing on 12 May against residential compounds left 35 people killed.
Since then there have been frequent clashes between police and suspects.
The kingdom has also banned dozens of shaikhs or Muslim preachers from performing sermons Riyadh deems are fuelling “terrorism”.
Diplomats have said this week’s raids are proof of Saudi Arabia’s seriousness in battling what they believe is rising extremism.