The charge relates to an alleged gesture made by the England international during Arsenal’s 6-3 Premier League defeat to Manchester City at the Etihad Stadium on Saturday.
Although the incident was not seen by match officials, it was captured on video and Wilshere has now been retrospectively charged by the FA.
A statement on the FA's official website, released on Tuesday, read: "Arsenal midfield player Jack Wilshere has been charged by The FA with making an offensive and/or insulting and/or abusive gesture.
"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.
"Wilshere has until 6pm on 18 December to respond to the charge."
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.
Should Wilshere accept his charge and be handed the same punishment, he would appear set to miss Arsenal's home game against fellow title contenders Chelsea on December 23.
