The Gunners submitted mitigating circumstances to the governing body, arguing the length of the mandatory punishment was excessive following Wilshere's admission after being retrospectively charged with misconduct.
Television cameras clearly showed the England international raising his middle finger in the direction of home supporters at the Etihad Stadium during the second half of the 6-3 Barclays Premier League defeat on Saturday, which was missed at the time by the match official. Had it not been, then referee Martin Atkinson would have shown Wilshere a straight red card.
In December 2011, Liverpool striker Luis Suarez was suspended for only 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.
However, a precedent had been set from earlier this season when a two-match suspension was handed out to Blackpool winger Tom Ince after he was retrospectively charged in relation to a gesture towards a match official in a Capital One Cup tie against Preston.
As such, the submissions from Arsenal were rejected and so Wilshere will now miss both the visit of Chelsea on December 23 as well as the Boxing Day trip to West Ham - by which time if results go against them Arsene Wenger's men could have been knocked off the top of the table.
A statement from the FA read: "Arsenal's Jack Wilshere has been suspended for two matches by an independent regulatory commission.
"Wilshere was charged by the FA with making an offensive and/or insulting and/or abusive gesture 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.
"Whilst admitting the charge, Wilshere claimed the standard sanction for this offence was clearly excessive. The commission rejected this claim and the two match suspension will commence with immediate
FA chairman Greg Dyke believes players like Wilshere, who turns 22 on New Year's Day, must take lessons on board from such regrettable instances.
"As a supporter I sympathise with the players because of the flak they get from the crowd," Dyke said on talkSPORT.
"People can lose their cool very quickly, but he (Wilshere) has got to learn.
"He is very well paid to play the game and he has got to learn to cope with it.
"You think back over many years of players who were hot-headed when they were younger, but not when they get older.
"They just learn and mature. That is what happens. It is part of life."
Arsenal will need to respond from their drubbing at City to avoid potentially being pushed down into fourth place for Christmas.
Defender Laurent Koscielny remains a doubt for Monday night's showdown with Chelsea after he suffered a deep gash in his knee just before half-time at the Etihad Stadium.
German forward Lukas Podolski, however, could be involved for the first time since late August following his recovery from a hamstring tear.
Midfielder Alex Oxlade-Chamberlain has targetted a return early in the new year having suffered a knee injury in the first game of the Premier League season against Aston Villa.
The 20-year-old England World Cup hopeful remains confident of a strong recovery, just as midfielder Aaron Ramsey has shown is possible after breaking his leg in two places during February 2010.
"You can either let setbacks be a setback or let them be a temporary setback as part of a learning curve to go on and turn it into something positive," he said.