The incident was not seen by match officials at the time, though video evidence has led to a potential retrospective ban with the incident deemed a "sending off offense".
Wilshere has until Dec. 18 to respond to the charge before facing a possible ban, which will include the Emirates Stadium clash with title rival Chelsea on Dec. 23.
A statement on the FA's official website reads: "Wilshere has been charged retrospectively by The FA under a new pilot project for potential ‘not seen’ incidents in Premier League matches.
"Under the new process, if an incident has not been seen by the match officials, a three-man panel will be asked by The FA to review it and advise what, if any action, they believe the match referee should have taken had it been witnessed at the time.
"For an FA charge to follow, all three panel members must agree it is a sending off offense. In this instance, the panel were unanimous."
Liverpool striker Luis Suarez received a one-match ban in December 2011 following an offensive gesture he made to Fulham fans during a Premier League match at Craven Cottage.