The Ivorian picked up the injury while playing for his country and last featured for United in the 1-0 defeat to Chelsea on November 5.
Mourinho said on Friday: “He goes to surgery, the decision is made. I don’t say [he’s out] for the rest of the season but it’s for the next two or three months.”
It means Bailly will be racing to be fit in time for United’s Champions League clash with Sevilla in February.
United currently trail rivals Manchester City, who record their 15th consecutive win of the season to beat the previous record of 14 on Wednesday, by 11 points. And Mouriinho is not in any doubt about the size of the task facing him.
“We go to clubs with a huge history where people look to the history and not to the moment and expectations are high,” he added.
“The job is difficult but I’ve had that experience before.
‘When I went to Real Madrid. They were in a difficult moment, no league title or cup, not even a Champions League quarter final for many years.”
“It was hard but it was good for my development as a manager too.”