The striker was shown a straight red card for a last-minute tackle on Stanislav Manolev and is facing a three-match ban.
But Arsene Wenger said after the game that Giroud had slipped as he challenged Manolev, and Arsenal hope to have the sending-off rescinded.
A statement on their website read: "Arsenal have lodged an appeal to the Football Association for the wrongful dismissal of Olivier Giroud during the Premier League match against Fulham at Craven Cottage on Saturday.
"An FA regulatory commission will hear the claim and make a verdict on Tuesday afternoon."
The FA could add a further game to Giroud's ban, ruling him out for the rest of the season, if they deem Arsenal's appeal frivolous.
Any suspension would leave Wenger's side short of strike options as they attempt to secure UEFA Champions League qualification.
Lukas Podolski, Theo Walcott and Gervinho all played up front earlier this season, but Giroud has started as a lone striker in each of the past nine games.