The Belgium international was shown a straight red card by referee Mike Dean after 76 minutes following a challenge on Arsenal midfielder Jack Wilshere.
City boss Roberto Mancini said immediately after the game that the reigning Barclays Premier League champions would appeal the decision and the club have confirmed they are seeking to have the dismissal overturned.
Mancini questioned the decision and claimed Kompany had not even committed a foul when challenging Wilshere.
If the appeal is unsuccessful and the three-match ban upheld City would be without their skipper for Premier League matches with Fulham and QPR and an FA Cup fourth-round tie against either Crystal Palace or Stoke.
"We will appeal, because it is impossible that we can lose one player for three games for nothing. It is not a red card, it is nothing," he said.
"He went into the tackle, anticipating the opponent and took the ball before.
"I don't know how it is possible to get a red card like this. It was no foul, no red card."