The 27-year-old Argentine international injured his hamstring in the 3-0 defeat at Liverpool on Monday and, after initial hopes he could make a quick recovery, is now likely to be sidelined for much of the Premier League run-in.
"Tevez is not available for Saturday. I think he will recover in three or four weeks. It is a big problem but we cannot take any risks," Mancini told a news briefing.
"We have six games left and hopefully we can get Carlos back for the last two or three games."
Tevez has played a major part in City's assault on a Champions League place with 19 league goals this season, and although they are fourth, Mancini's side are only three points ahead of Tottenham Hotspur who have a game in hand.
"I still have to decide what to do," he said. "But both players know this is an important chance for them."
