Sunderland's Darren Bent scored in the fifth minute of stoppage time on Saturday to give the home side a 1-1 draw, provoking Wenger's wrath.
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The 60-year-old Frenchman lost his cool and angrily remonstrated with match officials, furious over the time added on by referee Phil Dowd.
In a statement on its website the FA said Wenger had been charged with "using insulting and/or abusive language and behaviour amounting to improper conduct".
Under the FA's new fast-track procedures he has until Thursday to respond to the charge.
Wenger has been offered a standard sanction of a one-match touchline ban and an 8,000 pounds fine should he accept the charge.
If he denies the charge the case will be heard by a regulatory commission. The fourth official had indicated a minimum of four minutes additional time on Saturday.
Bent's goal, with the last kick of the game, cancelled out Cesc Fabregas's first-half effort and denied Arsenal the chance of going top of the table for at least 24 hours.
