The 68-year-old Frenchman reacted furiously to referee Mike Dean’s decision to award a penalty to West Brom in the 89th minute for handball by Calum Chambers.
The FA said the charge against Wenger was for his conduct in the match officials’ dressing room after the final whistle — he has till 1800GMT on Friday to respond to the charge.
Wenger did not sound repentant earlier on Tuesday at his press conference on the eve of their game with Chelsea.
“It was very disappointing,” Wenger said.
“What is more frustrating for me is it happened many times this season — at Stoke, Watford, Man City, now West Brom.
“It is a concerning coincidence for me.
“That is why as well I was not at all happy with the movement the referee made as to why he gave the penalty. It did not correspond at all with what happened.
“On that front it’s a bit worrying. He saw what he wanted to see.”