Activist Samar Badawi says Shaima Ghassaniya was found guilty Tuesday of driving without the government's permission.
No laws prohibit women from driving, but conservative religious edicts have banned it.
The ruling comes just two days after Saudi King Abdullah announced that, for the first time, women have the right to vote and run in the country's 2015 local elections.
Najalaa Harriri, who is also facing court for driving, told The Associated Press she needed to drive to take better care of her children.
Tuesday's verdict is the first of its kind in Saudi Arabia. Other women were detained for several days, but had not been sentenced by a court.