The French striker caught the ankle of Cottagers defender Stanislav Manolev when stretching for the ball and referee Andre Marriner, who had already sent off Steve Sidwell after 12 minutes for the home side, duly sent the Gunners star down the tunnel.
Speaking after the game, Arsene Wenger said that he had no complaints with the decision to dismiss Giroud, telling Sky Sports: "It looked like it [a deserved red card].
"I spoke with Giroud and he said he slipped when he went for the ball. I don't complain about the decision. We have to find a solution up front now for the final games but that can happen and we have to deal with that."
But Arsenal has now chosen to appeal to the Football Association in order to get the three-match suspension quashed ahead of the club's four remaining league fixtures.
The Gunners sit third in the Premier League table, one point ahead of Chelsea and two ahead of Tottenham, but the club has played one game more than its London rivals.