Wenger denied a charge of improper conduct and/or bringing the game into disrepute in relation to the comments he made after the 2-1 defeat by Chelsea on February 23 which ended with a mass brawl and three red cards.
"I don't agree with the report of the linesman because, for me, he lies," Wenger said in relation to the decision to send off Arsenal's Emmanuel Adebayor.
The commission found the charge to be proved, judging that the use of the word "lie" constituted improper conduct.
It was the third time this season the Frenchman had been punished by the FA.
Last month he was fined 2,500 pounds and warned about his conduct for arguing with a referee while in December he was fined 10,000 pounds, similarly warned and "severely censured" after a touchline row with former West Ham United manager Alan Pardew.
