The 31-year-old took a knock to his knee during training on Thursday and will not be risked. The Italian also revealed that Thiago Silva and new signing Lucas Moura, who joined from Sao Paulo this week, will also miss the game after being given the weekend off.
"Some players aren't ready to play. For example, Lucas has had only three days of preparation and is not ready," Ancelotti told reporters at a press conference.
“Alex, who's coming back from injury, Sylvain Armand and Gregory Van der Wiel are uncertain. Ibrahimovic suffered a knee knock in training. It's nothing serious but I don't want to take any risks."
Lucas, who has only had a few weeks off since the end of the Brazilian season in December, is expected to make his debut at home to Ajaccio on Friday and Ancelotti has already decided where the 20-year-old will fit into his team.
"He's fast, intelligent and plays it simple. This experience in Europe will permit him to become a fantastic player," he continued.
“He's used to playing wide but I think he can play in any of the attacking positions. To start with I will play him wide so as not to put him under too much pressure."
The former Chelsea coach then stressed the importance of the cup competition and remembered his side’s struggles against Locmine at the same stage last season.
"The French Cup is an important objective. Everybody knows the importance of the competition. It's a beautiful competition and everybody wants to win it," Ancelotti insisted.
“Last season, the first match against Locmine was very difficult and it will be the same on Sunday."