The campaign has been publicized on social networking sites, including Twitter, Facebook and YouTube, where women have been posting images of themselves driving.
The Women2Drive Facebook page, which includes messages of support from around the world, said the campaign would continue until a royal decree reversed the ban.
"All that we need is to run our errands without depending on drivers," said one woman in a film posted Friday, the BBC reports.
While there are no traffic laws that make it illegal for women to drive in Saudi Arabia, the ban is a religious fatwa imposed by conservative Muslim clerics.
“The driving ban is increasingly upsetting Saudi women, who now make up more than half of this country’s university students. Graduating in record numbers, they are looking for jobs and they want to drive themselves to work, to the shopping mall, to the grocery store and to their children’s schools,” wrote GlobalPost’s Caryle Murphy in a story suggested and voted on by GlobalPost readers.
“The new social media tools and recent peaceful street action in other Arab countries like Egypt have given the campaign quite a bit of steam,” Murphy wrote.
Supporters of the ban say it protects women, and prevents them from leaving home unescorted or travelling with an unrelated male.
Last month, a woman was arrested and spent more than a week in jail after driving a car and posting a video of herself online.
Manal Al Sherif, 32, was accused of "besmirching the kingdom's reputation abroad and stirring up public opinion." She was released after being forced to sign a form promising never to drive again.