The FA agreed Mane shouldn't have been sent off on Saturday when referee Lee Mason adjudged the Senegalese forward to have elbowed Stoke defender Erik Pieters in injury time.
After the match Southampton manager Ronald Koeman said: "The red card is a big mistake of the referee or maybe of the fourth referee or maybe the linesman.
"Sadio is trying to put his head to the ball. Even Pieters told me afterwards there was nothing."
Stoke boss Mark Hughes echoed Koeman's disbelief at the decision, saying: "I don't think that he has caught him. I think he has challenged for the ball. He hasn't thrown an arm or anything."
Mane will not now have to serve any suspension and will be available for Liverpool's visit on Sunday afternoon.