Last week Saudi women took to the driving seats of their cars to defy the ban, despite warnings that they could face punishment. Sixteen women were fined.
Colonel Fawaz al-Miman was quoted as having said six of the women were stopped in the Saudi capital Riyadh, and fined 300 riyals each (around £50).
Each of the women was made to “sign a pledge to respect the kingdom’s laws”, the capital’s deputy police spokesman said.
In Jeddah police fined two women for driving, a spokesman said, and Saudi newspapers reported that eight other women were stopped in Saudi Arabia’s eastern province.
A local daily newspaper, reported that a dozen women had been apprehended for defying the ban.
It quoted Saudi police as saying five of the women had been detained in Riyadh, three in the eastern city of Ahsa and two in Damman, and two in Jeddah.
The women arrested in Jeddah were both 50 years of age, a police spokesman was reported to have said, and one of them was accompanied by her 14-year-old child.
“They aggressively took it away from me, and I smiled back, and I walked away,” she said.
Saudi Arabia is the only country in the world that bans women from driving. Though there are no specific laws banning female drivers, authorities do not issue driving licences to women.
Activists said the women driving on Saturday had got licences from overseas.
In June 2011, around 40 women got behind the wheel in several cities in a protest sparked when a woman was arrested after posting a video of herself driving.
Another female driver was later arrested and sentenced to 10 lashes, but the king overturned the sentence.
Though Saudi Arabia has seen reform since then to reduce the gap between the rights of men and the rights of women, the male guardian system means women still need to obtain permission from a male relative to travel, get married, enrol in higher education or undergo surgery in some cases.