The ruling, although not officially confirmed, was tweeted by a Saudi princess and reported by AP news agency citing an unnamed official.
The woman, named as Shema, was found guilty of driving in Jeddah in July.
The sentence came two days after the king announced women would be allowed to vote for the first time in 2015.
“Thank God, the lashing of Shema is cancelled. Thanks to our beloved king,” tweeted Princess Amira al-Taweel, wife of Saudi Prince Alwaleed bin Talal.
“I am sure all Saudi women will be so happy.”
Two other women are due to appear in court later this year on similar charges, reports say.