The Portuguese manager confirmed the news in an interview with MUTV.
"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," Mourinho said.
"But now we have (Phil) Jones back and we have (Chris) Smalling, even (Daley) Blind, so it's a position we have good cover in but of course we'll miss the player."
Mourinho said he was not thinking about bringing in new players in the January transfer window to bolster his squad unless a suitable target becomes readily available.
"I'm not a big defender of the January market," Mourinho told a news conference on Saturday.
"But there are players and situations that sometimes you have the chance to do and you shouldn't lose that chance."
Second-placed United travel to 17th-placed West Bromwich Albion on Sunday.
