the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
There is nothing in Islamic Law that prohibits a woman from driving an automobile.
With respect to what is going on in Saudi Arabia, there is a principle in Islamic Law called sadd al-dharâ’i` (preventing the means to evil or harm). It is up to the leadership of the Muslim state to enact laws that prevent the spread of injury, injustice, and vice. These include speed limits and other traffic laws. Drivers must obey the speed limit, even though it is certainly not something set forth in the Qur'an and Sunnah.
In Saudi Arabia, the state considers it to be in the best interests of the people to enact laws restricting driving for certain sectors of the population, and that it falls within the state’s jurisdiction to do so. The law in Saudi Arabia that prevents women from driving is considered one of these laws. It is therefore not to be understood as an Islamic teaching.
This is all a question of public policy and not one of sacred law.
And Allah knows best.
Source: Islam Today