The former Chelsea midfielder has been a peripheral figure since arriving at Old Trafford in July last year, struggling with a loss of form and persistent injury issues.
The England international has played just 32 times for United so far, scoring a solitary goal, and has started just nine Premier League games in total.
United boss Ruben Amorim said the 25-year-old would be out for "several weeks" after being forced off early in last week's Manchester derby, which United won 2-1.
"I don't know the exact date, but it's going to be for a long time," he said. "And that's it. It's part of football and we continue."
The former Sporting Lisbon boss said he would try to help Mount, who has impressed in recent weeks, even while he is out of action.
"What I can do is to help Mase, to teach him how to play our game when he's recovering. Try to use that time for him to think in different things," he said.
"And then I think the worst part is that we don't have time to train like we should do when you are recovering from a lot of injuries.
"So we are always travelling, we have games, training, we don't have all the team together. And this is really hard to recreate the game before they come to the game."
Amorim said Marcus Rashford would be available for Sunday's home match against Bournemouth after being absent from the squad for the game against City and Thursday's 4-3 defeat to Tottenham in the League Cup quarter-finals.
The Portuguese manager insisted it was not a disciplinary issue.
Rashford, 27, admitted earlier this week that he was "ready for a new challenge" after being asked in an interview about his future at United.
Amorim, who replaced the sacked Erik ten Hag at Old Trafford last month, said he felt United were making progress, even though they are still a lowly 13th in the Premier League.
"I think we are improving near the opponent's box," he said. "We had some games that we are near the box, but without a real threat. You could see different things (against Tottenham).
"You can see that we can shoot. We are near the goal and you feel it, you really feel it. I think it's a good thing in our team. I feel that our team is faster, are pressing more.
"The physicality is improving, the understanding of the game and you can see it by the controlling of the game."
