The England international was pictured raising his middle finger towards the home supporters during Arsenal's 6-3 defeat at the Etihad Stadium on Saturday.
Liverpool's Luis Suarez was handed a one-match ban and a fine for a similar incident at Fulham in 2011, and Wilshere now faces a nervy wait to see if he will face retrospective action.
Elsewhere, team-mate Mesut Ozil has apologised to Arsenal supporters after failing to applaud them at the end of the match.
The 25-year-old headed straight towards the tunnel at the final whistle, and was given a verbal tirade by fellow Germany international Per Mertesacker for failing to recognise the Arsenal faithful who had made the trip to Manchester.
"Sorry I didn't thank the fans at the end of the game," Ozil posted on his official Facebook page.
"You have been brilliant to me and I know you had travelled a long way and spent your money to support us. I was upset with the result and I know I should have come to you to say 'thank you' and I know it is a big Arsenal tradition win, lose or draw."
