According to The Sun, Iwobi was caught on camera dancing in central London at 2.37am on Saturday morning and the video was uploaded to Snapchat.
The clip captioned, “Shouldn’t Iwobi be sleeping?” and shows the 21-year-old dancing and singing among a group of people.
It is understood that the group rented a flat in Soho and partied until 3.30am.
“If that is true he will be fined. It’s unacceptable,” Wenger told reporters on Tuesday morning.
Iwobi played the full 90 minutes as the Gunners suffered a shock 4-2 defeat at the City Ground.
Speaking on the defeat, Wenger said: “We won the FA Cup three times in the last four years. You have to expect it will not happen every year, but we did not produce the performance we expected.”