The Argentina international injured a hamstring in Monday night's defeat to Liverpool at Anfield and is expected to be out until next month.
"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."
It is a major problem for City given Tevez is by far their most prolific striker.
"We have six games left and hopefully we can get Carlos back for the last two or three games," added Mancini.
It means Tevez would be in with a chance of making the final on May 14 if City make it through to face either Stoke or Bolton.
However, Mancini will be forced to rely on either or both of Edin Dzeko and Mario Balotelli to derail United's Treble bid.
"I still have to decide what to do," said Mancini. "But both players know this is an important chance for them.
"Every player knows this is an important moment for the club.
"If we will we can go to a final, so every player will give 100%."
Source: PA
Source: PA