Huddlestone was shown a red card in the dying minutes of Saturday's 1-1 draw with Norwich following a challenge on midfielder Jonny Howson.
Referee Mark Halsey deemed the tackle to be dangerous but Tottenham appealed against the red card and learned on Tuesday afternoon they had been successful.
An FA statement read: "Tottenham Hotspur’s Tom Huddlestone has had his claim for wrongful dismissal upheld.
"As a result, the three-match suspension handed to the midfielder has been withdrawn with immediate effect.
"Huddlestone had originally received a red card for serious foul play in his side’s 1-1 draw at home to Norwich City on Saturday 1 September 2012."