Routledge was sent off for violent conduct in the 86th minute of the Swans' 1-1 draw with QPR at Loftus Road on New Year’s Day.
Referee Anthony Taylor handed Routledge a red card after he reacted to a tackle by QPR midfielder Karl Henry in the Premier League game.
Swansea manager Garry Monk was left fuming with the officials after the game, describing it as a "leg-breaker" tackle and confirming his intention to appeal against the decision.
The club have now been successful with their appeal and Routledge’s three-match suspension has been withdrawn with immediate effect, meaning he is available for Saturday’s FA Cup third-round tie against Tranmere.
Swansea were trailing 1-0 at the time of Routledge’s dismissal but, despite being down to 10 men, they still managed to snatch a point thanks to Wilfried Bony’s last-gasp goal.