City boss Roberto Mancini had wanted the Ivorian and his brother, defender Kolo, to play in the showpiece tie but Zahoui has refused to disrupt his own preparations.
Toure told The Sun: "I am very sad. Missing the FA Cup derby is a real pain after I have spent weeks trying to seek a solution.
"But the federation would not accept us leaving it to Sunday. I am suffering a lot over this."
Ivory Coast will begin their warm-up period for the tournament in the United Arab Emirates, ahead of friendlies with Lebanon and Tunisia, before the competition starts in Equitorial Guinea and Gabon.
The Elephants will then take on Sudan, Burkina Faso and Angola in Group B as they look for their second AFCON title.