Argentine is out for up to a month after sustaining the problem in Monday night’s defeat against Liverpool, and could even miss the clash for fourth place against Tottenham
The Argentine sustained a hamstring injury during the recent 3-0 defeat to Liverpool, and had to be replaced after only 15 minutes.
Now the Italian boss has confirmed that the former West Ham United man will be out of action for "three or four weeks".
"Tevez is not available for Saturday," Mancini said.
"I think he will recover in three or four weeks. It is a big problem but we can't take any risks."
Apart from the clash against United, Tevez is also expected to miss the games against Blackburn Rovers, West Ham United and Everton, and could even miss the clashes with Tottenham and Stoke City.
Mancini added: "After this game we have another six, so hopefully we have him for the last two or three matches.
"Every player knows this is an important moment for the club."
Concerning the game against Sir Alex Ferguson's men, Mancini maintained that he has not yet arrived at a decision as to whether Balotelli or Edin Dzeko will replace the injured Tevez.
"I have not decided the first XI, we have another 48 hours," he said. "Mario, or Edin, or both players - they both have an important chance. I trust my players."
For now, however, the manager believes that a semi-final appearance is a cause for celebration, as the Eastlands outfit have gone over three decades without any major silverware.
He said: "We should be happy because for this club it's been a long time since we made the semi-finals. We have a good chance.
"I think the fans should be happy for our situation and for this game but we need to concentrate and focus. It's a semi-final, it's very important but we know it's a difficult game."
Follow Goal.com on to get the latest soccer news directly. Check out Goal.com's page; be part of the best soccer fan community in the world!