Television pictures appeared to show the Gunners midfielder, 21, raising a finger towards the crowd during the 6-3 defeat at Etihad Stadium.
The Football Association will await referee Martin Atkinson's official report before deciding whether to review the incident or not.
"If he did it and he is banned then we will have to accept it," Wenger said.
"I don't know if he did it."
Liverpool striker Luis Suarez was suspended for one match, fined £20,000 and warned as to his future conduct after admitting an FA charge of improper conduct in 2011.
Suarez, 26, raised the middle finger of his left hand as he walked off the pitch following a 1-0 defeat at Fulham.
Wilshere appeared to raise a finger towards the crowd on 68 minutes after disagreeing with a decision to award City a goal kick.
Former Arsenal defender Martin Keown, talking on BBC One's Final Score programme, said: "It's unfortunate that Jack Wilshere is involved in that sort of thing, and Wenger is right - it needs to be stamped on. We don't want that.
"We don't want Jack to go over the line. He is representing Arsenal and you have to remember who you are and what you are at all times."
Arsenal manager Arsene Wenger admitted Jack Wilshere may have to accept a ban for an apparent abusive hand gesture.