Eysseric was hit with the 11-game ban by the disciplinary committee of the Ligue de Football Professionnel (LFP) after Clement was left with a fractured fibula as a result of his wild lunge.
Eysseric was shown a straight red card after the incident in the 24th minute of a 4-0 home victory for Saint-Etienne, with Clement receiving lengthy treatment on the pitch at the Stade Geoffroy-Guichard before being taken to hospital.
Clement, 28, faces five to six months of rehabilitation after undergoing successful surgery.
Nice confirmed Eysseric's suspension in a short statement on their website.
"The player will therefore not play again this season."
Eysseric has apologised for his actions and already confirmed he would not appeal the punishment handed down by the LFP.
In quotes reported by L'Equipe, Eysseric said after the hearing: "I explained my feelings and my actions. They all listened.
"I have nothing to say about the penalty, it is their decision."