This is a very big test for the Saudi royal family. It's the largest in the world and its members range from liberals to hardliners and they are divided on this issue.
One of the hardliners, Prince Naif, the Minister of the Interior, is reported to have said on several occasions that women will never drive. But the regime is also practical and cares about world opinion – and this really doesn't look good.
Saudi Arabia boasts of its modernity as the largest oil producer in the world, but this oil is a curse if it comes before democracy.
Oil supports the patriarchal system. The generation of mothers before the 1950s, when the oil revenues started to come, had traditional occupations. Now they are put in gilded cages. Not all of those cages are gilded of course: there are hundreds of thousands who cannot afford a driver.
The House of Saud has aligned itself with the hardline Wahhabi establishment, which has asserted control over women's education, and their confinement.
But now pressure is mounting in the country. Many of these women have driving licences from Egypt, Lebanon and other Arab countries. No wonder they question strongly why their neighbours can drive and they cannot.
Saudi women have watched their peers in the other Arab nations – including conservative places like Yemen protesting – and they are not going to sit back and accept this ban, which is not justified by any Islamic text.
This extreme segregation cannot be justified on religious or economic grounds. Many women have signed petitions saying: "If I earn $1,000, I don't want to give $500 to a driver". There are so many contradictions and it's such a problem for the Saudi regime.
I recently had an email from a woman in Mecca, who called herself Fatima, who said a woman can't even give birth without being accompanied by a male guardian to the hospital. A woman also cannot leave the country without having a letter from a male guardian.
This is a legitimate demand and a basic human right. This is about a woman wanting to get into a car to buy a pint of milk for her child. She cannot even do this. A woman can study medicine and can become a medical doctor, but if her child is ill in the middle of the night, she can't drive her to a hospital.
If this ban is ended, it could lead to bigger change such as women asking for the right to vote and could lead to a new political force and the fracture of dictatorship.
Mai Yamani is the author of Changed Identities: The Challenge of a New Generation in Saudi Arabia