Wilshere admitted an FA charge over the offensive hand gesture made towards Manchester City fans, but contested the mandatory two-match ban and the case was heard by a commission on Thursday.
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 defeat on Saturday.
Although the incident was missed at the time by referee Martin Atkinson and his officials, the FA were 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, it would have merited a dismissal.
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.
England international Wilshere will miss the showdown with Chelsea at Emirates Stadium on December 23 and also the Boxing Day fixture at West Ham.