He said: "Now at least it opens the door for discussion on the guardian system.
'Women are independent and can take care of themselves."
The order is the latest in a series of steps taken by Saudi Arabia to include women more in the workforce as the kingdom moves to diversify its economy and reduce its reliance on oil.
The trend started in 2011 when the late King Abdullah allowed women onto the government advisory Shura Council.
Women can now vote in municipal elections, work in some retail and hospitality jobs and were allowed to compete in the Olympics for the first time in 2012.
But Saudi Arabia was still ranked 141 of 144 countries in the 2016 Global Gender Gap, a World Economic Forum study on how women fare in economic and political participation, health and education.
The system of male guardianship, which requires women to obtain permission from a father, husband, or son to travel, study or marry is an impediment to realising women's rights, say rights groups.
Mr Akeel said: "Male guardianship is un-Islamic and humiliating for women.
'Some (men) take advantage of this male guardianship for their own benefit and abuse it."