The Algerian Football Federation (FAF) said 19-year-old Arsenal midfielder Bennacer will arrive in Algiers on Thursday before flying to Gabon for their tournament opener on Sunday against Zimbabwe.
Taïder aggravated a previous injury during training with defender Ramy Bensebaini also nursing a niggling knee problem.
“It’s a real pity for Taider, it happened at the last minute. He was a key element for me, a player who had experience in the Cup of Nations and World Cup,” said Algeria coach George Leekens.
“I hope that Ismael Bennacer will be up to the task. He will learn a lot in this CAN.
Algeria are drawn in Group B with Tunisia, Senegal and Zimbabwe, with the top two advancing to the quarter-finals.
Download our app and read this and other great stories on the move. Available for Android and iOS.