Midfielder Eysseric was hit with the 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 last weekend.
Eysseric was shown a straight red card following the incident in the 24th minute of a 4-0 home victory for St 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 this evening, saying: "Valentin Eysseric, who was sent off at St Etienne last weekend, was suspended for 11 games by the French Professional League's (LFP) disciplinary committee. 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."