Brown was dismissed for a foul on Charlie Adam in the first half at the Britannia Stadium, shortly after the Scotland international had scored the opening goal.
The decision left Sunderland manager Gus Poyet fuming and the club decided to appeal the decision.
That has now been upheld by the FA, who released a short statement on their official website to confirm the card had been rescinded.
"With regard to Brown, who was dismissed for serious foul play during Saturday's game at Stoke City, the claim was upheld," it read.
"As a result, his three-match suspension has been withdrawn with immediate effect."
Centre-back Brown will now be free to play in the Premier League game with Aston Villa on Saturday.