Television cameras picked up Wilshere raising his middle finger in the direction of home supporters at the Etihad Stadium during the second half of the Gunners' 6-3 Barclays Premier League defeat on Saturday.
Although the incident was missed at the time by referee Martin Atkinson and his officials, the FA was able to retrospectively implement disciplinary proceedings against the player under a new pilot scheme for 'not seen' incidents in Premier League matches.
As such, an independent three-man panel agreed if the gesture had been viewed during the game, then it would have merited a dismissal.
However, with the precedent of a two-match suspension handed out to Blackpool winger Tom Ince when he retrospectively charged in relation to a gesture towards a match official in a Capital One Cup tie against Preston earlier this season, Press Association Sport understands Arsenal have submitted mitigating circumstances to the governing body, arguing the length of the punishment is excessive.
In December 2011, Liverpool striker Luis Suarez 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.
An FA disciplinary commission will now consider Wilshere's case when it meets later on Thursday, and make a definitive ruling on the length of suspension which must be served.
If the two-match mandatory punishment is upheld, then the England international would miss the showdown with Chelsea at the Emirates Stadium on December 23 and also the Boxing Day fixture at West Ham.
On the pitch, Wenger is expecting a reaction to the loss at Manchester City, as his side look to retain top spot over a weekend which, if all results go against them, could see Arsenal drop to fourth.
Defender Laurent Koscielny remains a doubt for the Chelsea match, after he suffered a deep cut to his knee in the build-up to City's second goal, and was not able to play on in the second half.
If Arsenal are to last the distance in the championship race, then more is needed from club-record signing Mesut Ozil, according to former Liverpool and England forward Michael Owen.
Ozil, signed on deadline day from Real Madrid for £43million, has scored four goals and created many opportunities for Arsenal as he settles into the English game.
However, Owen - who also used to play for the Spanish giants - feels the German playmaker lacks consistency at the highest level.
"[Arsenal] don't have the class of player to go toe to toe with the main title contenders," Owen said on his 'half-term report' blog on sport social network www.sportlobster.com.
"Despite people constantly telling me Mesut Ozil is world class, his inconsistency means that we only see occasional glimpses of real quality.
"His odd good performance is usually followed by half a dozen poor ones."