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 Premier League champions would appeal the decision and the club have confirmed on Monday morning that they are seeking to have the dismissal overturned.
Speaking after the game, Mancini questioned the decision and claimed Kompany had not even committed a foul when challenging Wilshere.
"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."
Kompany also later took to Twitter to defend the challenge but stopped short of criticising Dean.
He wrote: "First. Massive congrats to our team and fans, great game! Also. No grudges against the referee, I understand the difficulty of the job.
"About the tackle: If the ball is overrun by the opponent and a 50/50 challenge occurs, collision is inevitable.
"Ultimately I'm a defender: Appeal may work or not. I will never pull out of a challenge, as much as I will never intend to injury a player."
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.