The 31-year-old received a straight red card for his reckless first-half challenge on Enner Valencia and will therefore miss Saturday's FA Cup final against Chelsea and the first two domestic fixtures of next season.
Arsenal beat Everton 3-1 despite his dismissal, but his confirmed absence is a further disappointment for manager Arsene Wenger, who also has fitness concerns over fellow defenders Gabriel Paulista and Shkodran Mustafi.
"Laurent Koscielny will serve a three-match suspension with immediate effect after a claim of wrongful dismissal was unsuccessful," an FA statement read.
"The Arsenal defender was sent off for serious foul play during the game against Everton on Sunday (21 May 2017).
"An independent regulatory commission heard the case today (Tuesday 23 May 2017)."
Source : PA