Television cameras picked up Wilshere raising his middle finger in the direction of Manchester City supporters at the Etihad Stadium during the second half of the Gunners' 6-3 defeat.
Journalists understand the FA took its time to gather evidence to understand the context of the situation having received the observations of referee Martin Atkinson and his officials on Monday, and have now decided there is a case to answer.
Such sanctions have been implemented in the past as was the case with Liverpool striker Luis Suarez, who was suspended for one match, fined £20,000 and warned as to his future conduct after he made a gesture to home fans as he walked off the pitch following a 1-0 defeat at Fulham in December 2011.
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 and have to pay a fine.
A statement from the FA read: "Arsenal midfield player Jack Wilshere has been charged by the FA with making an offensive and/or insulting and/or abusive gesture.
"The charge follows an alleged gesture made during the fixture between Manchester City and Arsenal at the Etihad Stadium on Saturday 14 December. The incident was not seen by 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.
"Wilshere has until 6pm on 18 December to respond to the charge."
Wenger has challenged his side to produce a response from their defeat at City, where defensive frailties were unearthed once more.
However, by the time the Gunners kick off against Chelsea, they could already be off the top of the table.
Indeed, should Liverpool beat Cardiff at Anfield in Saturday's lunchtime kick-off, followed by a City win at struggling Fulham, then Arsenal would be down in third place on goal difference.
Chelsea, currently two points adrift, could also usurp Wenger's men if Jose Mourinho records another victory over the French coach, while Everton could also close to within a point if they overcome Swansea the Liberty Stadium on Sunday.
The loss at City was a second on the spin for Arsenal, who went down 2-0 away to Napoli last Wednesday night as hopes of finishing top of their Champions League group evaporated.
Consequently, Arsenal were unseeded and so will face holders Bayern Munich in the last 16, the same stage at which they were knocked out by the Germans in 2013.
Wenger, though, says his side will have "nothing to lose" when they face off early next year, with the second leg set for the Allianz Arena where Arsenal recorded a famous 2-0 win last season, only to go out on aggregate.
Arsenal defender Laurent Koscielny remains a doubt for the Chelsea match, having suffered a deep cut to his knee when attempting to prevent City's second goal late in the first half on Saturday and was unable to continue.