Female driver Azza Al Shmasani alights from her car after driving in defiance of the ban in Riyadh, June 22, (Reuters).
"A girl who was driving, accompanied by her brother in Jeddah's southern neighbourhood of Al-Suleymania, was arrested," Saudi news website Sabq.org reported.
"The two were surrounded by four police patrols who asked for their identities then took them to a police station, where they were interrogated," said the website.
It added that "the police were tipped-off by residents who claimed to have seen an unveiled woman driving" in the Red Sea city.
Meanwhile, in posts on the social networking website Facebook, activists said members of Saudi Arabia's religious police arrested four women testing the driving ban at a members-only resort in northern Jeddah on Tuesday.
AFP could not independently verify the reports and it was unclear if the women are still being held. Last week, two Saudi women said they drove their cars in the Gulf kingdom.
Their actions came in response to a call on the Internet for women in Riyadh to get behind the wheel, after a show of defiance on June 17 in which 42 women took to the road.
US Secretary of State Hillary Clinton and German Chancellor Angela Merkel have both expressed support for Saudi women who wish to drive.
No law forbids women from driving in Saudi Arabia but a religious edict, or fatwa, stipulates that women must be driven by male chauffeurs or members of their family.