The striker was shown a straight red card for serious foul play for a last-minute challenge on Stanislav Manolev at Craven Cottage.
Arsene Wenger said after the game Giroud had slipped as he went to tackle Manolev, and an appeal was lodged with the Football Association.
But that explanation has cut no ice with an Independent Regulatory Commission, and Giroud will sit out games against Manchester United, QPR and Wigan.
The FA decided against adding a further game for a frivolous appeal, so Giroud will be available for Arsenal's final game of the season at Newcastle.
But the France international's absence leaves Wenger short of strike options as he attempts 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.
Third-placed Arsenal lead Chelsea by a point and Tottenham by two, but both their London rivals have a game in hand.