Gervinho was hurt during training with his Chinese club Hebei Fortune last month but only underwent surgery in Paris last week.
"The operation was successful but his recovery will be between four to six months which means he is out of the Nations Cup," an Ivorian Football federation statement said.
The Ivory Coast will be defending their title at the tournament in Gabon in January.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Reporting by Mark Gleeson in Cape Town; Editing by John O'Brien)
