"It is alleged his language and/or behaviour in the match officials’ changing room after the game was abusive and/or improper and/or questioned the integrity of the match referee," the FA said in a statement.
Wenger has until Friday to respond to the charge.
The Frenchman was handed a four-match ban for misconduct last January for pushing the fourth official after his team's 2-1 win over Burnley, and risks another suspension for his latest outburst.
Sunday had seen Wenger surpass former Manchester United manager Alex Ferguson’s Premier League record with his 811th game in charge at one team, but that was soured by the outcome.
Dean awarded an 89th minute penalty after Calum Chambers was adjudged to have handled in the area, with Jay Rodriguez converting to deny Arsenal victory and provoke a furious reaction.
Wenger, whose team saw out 2017 in fifth place, was spoken to by Dean.
"I did fight many years ago for referees to become professional, but unfortunately their levels do not go up. It is difficult to accept," the manager told Sky Sports afterwards.
(Reporting by Alan Baldwin, editing by Jeremy Gaunt)
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