Nassima al-Sadah is the third woman to file such a lawsuit this year over the rule which enforces a traditional ban on women driving in the Muslim desert nation.
"I filed the lawsuit against the traffic department of the interior ministry at the Dammam court" in Eastern Province, she told AFP.
Before her, Manal al-Sharif, who became a symbol of a campaign to drive after she was arrested last year for defying the ban, and rights activist Samar Badawi also filed similar lawsuits.
Sadah said she made a point by trying repeatedly to apply for a driving licence at the traffic department in Eastern Province.
Saudi Arabia is the only country in the world that bans women from driving.
In June 2011, women activists launched a Women2Drive campaign on social media networks, with many also braving the ban and posting videos of themselves driving.
The following June, activists cancelled plans to get behind the steering wheel on the first anniversary of their campaign, opting instead to petition King Abdullah to lift the ban.
Their campaign, which spread through Facebook and Twitter, was the largest mass action since November 1990, when 47 Saudi women were arrested and punished after demonstrating in cars.
Women in the kingdom who have the means hire drivers, while others must depend on the goodwill of male relatives.
They are also obliged to be veiled in public, and cannot travel unless accompanied by their husbands or a close male relative.