The charge relates to an alleged gesture made by the England midfielder during the 6-3 Premier League win by Manchester City at the Etihad Stadium on December 14 - the incident was not seen by the match officials but was caught on video.
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 offence. In this instance, the panel were unanimous.
The Arsenal midfielder has until 6pm on December 18 to respond to the FA charge.
Gunners boss Arsene Wenger admitted in his post-match press conference that the club would accept any ban handed out "if he did it".
If that is the case, then Wilshere is likely to miss the visit of Chelsea to the Emirates Stadium next Monday.