The former Sweden international has been struck down by a knee injury suffered in the goalless draw with Southampton a fortnight ago.
Ibrahimovic, unable to find his rhythm since returning from a long-term problem to the same knee last year, will now spend time recovering before beginning to build up fitness once again in a couple of weeks' time.
"Zlatan is injured or not totally happy with his condition," Mourinho told reporters. "He consulted our doctors and made the decision to stop. The date for him to be back training with the team is around the end of January and beginning of February."
Since signing a one-year contract extension with United earlier this season, Ibrahimovic has managed just one goal in seven appearances.