McGugan, 20, sustained the injury in an accidental first-half collision with the Watford goalkeeper Scott Loach in Tuesday's 4-2 home defeat against the Hornets.
He will have the operation next week when the swelling on the left-hand side of his face has gone down.
McGugan has been told to expect his rehabilitation time from the date of the operation to be between a month and six weeks.
When he is given the all-clear to resume playing, he will have to wear a protective mask for two months.
Source: Team_Talk