The official declined to elaborate. He spoke Wednesday on condition of anonymity because he was not authorized to brief the media.
A day earlier, a Saudi court found Shaima Jastaina guilty of violating the driving ban, and sentenced her to 10 lashes.
It was the first time a legal punishment had been handed down for breaking the longtime ban in the ultraconservative Muslim nation. No laws prohibit women from driving, but conservative religious edicts have banned it.
Earlier this week, King Abdullah announced that women will have the right to vote and run in the country's 2015 local elections.