The Belgian centre-back was sent off by match official Mike Dean for a tackle on Jack Wilshere in the second half at the Emirates Stadium.
"An Independent Regulatory Commission has today upheld a claim of wrongful dismissal regarding Manchester City’s Vincent Kompany," read an FA statement released on Tuesday.
|MANCHESTER CITY LATEST
|Evens||Manchester City are evens with Bet365 to keep a clean sheet against Fulham
Manchester City boss Roberto Mancini had indicated after the game that the club would protest the decision before an appeal was officially lodged on Monday.
"This is not a red card, absolutely not," the Italian told Sky Sports.
"He has one foot to take the ball, the other is left. I think that the referee made a mistake there.
"It was not a sending-off for Vinnie because Vinnie took the ball with only one foot after anticipating the opponent."
Arsenal were already down to 10 men following Laurent Koscielny's dismissal in the early stages for hauling down Edin Dzeko in the Gunners' penalty area.