Arsenal manager
The Frenchman was angry after referee Mike Dean gave the Baggies a last-minute penalty, which they scored.
It is alleged the 68-year-old's conduct in the match officials' changing room was abusive and that he questioned the integrity of the referee.
Wenger has until 18:00 GMT on Friday to respond to the charge.
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Last January, Wenger was given a four-match touchline ban by the FA after being found guilty of misconduct after an incident with fourth official Anthony Taylor during a league game against Burnley.
Credit: BBC