The Super League club carried out a two-week internal investigation after learning of the incident, which took place on May 27.
A statement from the club confirmed that Bateman's ban has been backdated to the time of the incident, meaning that he will be available for selection on July 22.
Chairman Ian Lenagan said: "It is difficult to take such disciplinary action but we are responsible for the behaviour of Wigan players and the good name and reputation of Wigan Rugby League Club and all that it stands for. Disciplinary action needed to be taken and to be seen to have been taken.
"John Bateman has expressed his full regret at the incident, as have other parties, and the club will be working hard with John to ensure that he learns properly from the experience and comes back stronger than ever. He will remain a Wigan player and return to training during the period.
"Kris Radlinski and Shaun Wane are confident that the spirit and togetherness of the squad is at a high level, which has been illustrated by the fact that two difficult wins were achieved during the period of investigative distraction. The incident is now viewed as closed and no further comment will be made by club or players."
Bateman has also been fined £10,000.