The FA handed Wilshere a two-match for the gesture, which came during the second half of the Gunners' 6-3 defeat at the Etihad Stadium.
The England midfielder missed Monday's 0-0 draw against Chelsea and he will also sit out the Boxing Day clash at West Ham.
Wilshere, who has two children, admits he made a mistake in getting riled by the supporters who abused him, and he is braced for more barracking from the stands in the future.
Wilshere tweeted: "Gutted not to be Involved last night! Shouldn't of reacted the way I did but I know all you dads out there love your kids the way I do...
"Suppose I will just have to take the abuse about my kids in future......anyway, one more game to go! Can't wait to be back! #AFC"