French striker Giroud was dismissed by referee Andre Marriner in the 90th minute of the London derby at Craven Cottage for jumping into a challenge with Stanislav Manolev.
"We have lodged an appeal to the Football Association for the wrongful dismissal of Olivier Giroud against Fulham," read a statement on the club's official website. "An FA regulatory commission will hear the claim and make a verdict on Tuesday afternoon."
If the appeal is unsuccessful, Giroud will receive a three-match ban for the straight red card.
Replays showed the £13million summer signing from Montpellier, who has scored 17 goals for Arsenal, made contact with the ball during the tackle.
Arsene Wenger hinted after a win that lifted the Gunners to third in the table that an appeal would be made.
"Giroud told me he did slip and went a bit over the ball," the Arsenal boss said
"Knowing that Steve Sidwell had been sent off, when the referee went to see him, we knew it would be a red card.
"We will have to deal with that now because he will miss three games and that is not easy for us to cope with.
"Nobody would say Giroud is a dirty player, it is purely accidental, but sometimes accidental can be dangerous."