He has also been fined £40,000.
The nice thing is that the suspension starts immediately - he'll miss Sunday's Cup match against Forest and the Carabao Cup semifinal against Chelsea on Wednesday, and the only league game he'll miss is Bournemouth next Sunday.
Wenger admitted using abusive and improper language towards the match officials and questioned the integrity of the referee following the clash last Sunday.
The Arsenal defender was penalised after Kieran Gibbs appeared to push the ball onto his arm, with Wenger feeling his star's action was not deliberate.
Arsene Wenger stands by referee remarks
Both Premier League matches ended as draws and Wenger now has until 6pm on Tuesday to respond.
Part of his anger stemmed from a penalty the away side won when Eden Hazard was deemed to have been fouled by Hector Bellerin by referee Anthony Taylor - a decision branded "farcical".
"I maintain what I said in the press conference - 100 per cent", the Frenchman said. Nothing has changed. I've been in England for 21 years and I've tried to serve this game with honesty, integrity and when I have something to say, I say it.
Wenger said before the game against Chelsea: "I must say what is more frustrating for me is that it happened many times this season - at Stoke, at Watford, at Manchester City, at West Brom. I'm quite surprised that that is shocking".More news: Kyrgios through to Brisbane final