Diabate has nine goals in all competitions for the Ligue 1 side this season and had been named in Henryk Kasperczak's squad for the African showpiece, which begins later this month.
However, the 26-year-old will now miss the tournament in Equatorial Guinea and could be sidelined for up to four months.
"Following consultation with Dr. Jean-Pierre Franceschi and in agreement with Dr. Thierry Delmeule, Cheick Diabate will undergo an operation that is essential for the successful continuation of his career," read a statement from Bordeaux.
"His unavailability will be around four months."
Kasperczak has Cheick Fantamady Diarra, Souleymane Diarra, Abdoulaye Samake, Kalifa Traore, Idrissa Traore and Mohamed Traore as reserves, but no replacement has been named.
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