Koscielny was sent off by referee Mike Oliver for a late challenge on Enner Valencia on the last day of the season during the match against Everton which they won 3-1.
Koscielny will serve a three-match ban, the first game of the ban will be Saturday's FA Cup final against English Premier League Champions Chelsea FC at the Wembley Stadium.
Arsenal are facing a defensive crisis for the final, with Arsene Wenger also expected to be without Gabriel after the defender was substituted due to injury against Everton.
Per Mertesacker came off the bench to make his first Premier League appearance of the season, while Shkodran Mustafi missed the Everton game with a head injury sustained in Arsenal's victory over Sunderland.
Alexis Sanchez was also substituted in the second half of the Everton match, with the Chilean forward limping out of the game with 22 minutes to play.
Laurent Koscielny will serve a three-match suspension after his wrongful dismissal claim was rejected: https://t.co/VDPrW3jT3H— The FA (@FA) May 23, 2017