The Belgian defender was dismissed in the 76th minute at the Emirates Stadium by referee Mike Dean for a two-footed challenge on Arsenal midfielder Jack Wilshere.
City manager Roberto Mancini said immediately after the game that the club would appeal against the dismissal.
The official Manchester City website has confirmed that the club has registered an appeal on behalf of Kompany, who would miss three games because of the straight red card.
Kompany won the ball in the challenge and took to Twitter to defend his tackle, saying: "About the tackle: If the ball is overrun by the opponent and a 50/50 challenge occurs, collision is inevitable."
The central defender has received support from former defenders such as ex-Liverpool captain Alan Hansen and Robbie Savage, who was renowned for tough tackling during his career with Leicester City and Blackburn Rovers, among others.
However, the Daily Mail has reported that any appeal against the dismissal will be unsuccessful with the Football Association.
A year ago, Kompany was involved in a similar situation when he was shown the red card during an FA Cup third-round tie against Manchester United for a challenge on Nani at the City of Manchester Stadium.
Kompany was sent off just 12 minutes into the cup-tie and United took full advantage and went on to win 3-2.
The City captain is now facing another spell on the sidelines after his dismissal on Sunday.
Did Kompany deserve to be dismissed against Arsenal or is tackling becoming an endangered skill?
Let us know what you think.