From the BBC

(...)The ban on women drivers, while informal, is enforced by Saudi police through fines and arrests. Only men are permitted to acquire driving licences. 

"If a woman drives a car, not out of pure necessity, that could have negative physiological impacts as functional and physiological medical studies show that it automatically affects the ovaries and pushes the pelvis upwards," Sheikh Lohaidan told the news website Sabq.org.

"That is why we find those who regularly drive have children with clinical problems of varying degrees."

Source

I am all for religious freedom. Obscurantism is another matter altogether.