The Hoops skipper will not recover in time for his team's Champions League last-16 trip to Turin where the Scottish side will aim to come back from a 3-0 home defeatCeltic midfielder Scott Brown will miss the Scottish side's crunch Champions League second leg match in Juventus.
The Hoops will have to overturn a 3-0 deficit to reach the next round, and will need to do it without their captain as Brown is still suffering from an abductor injury that has kept him out of several games recently.
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Celtic boss Neil Lennon told reporters: "[Scott] is out indefinitely.
"We are still waiting to hear from the specialist, whether it requires surgery or not and I am hoping that we will get a definitive answer by the end of the week."
Lennon also spoke about the returns of defenders Mikael Lustig and Charlie Mulgrew from their own injury lay-offs.
The Northern Irishman added: "Lustig is still out and Charlie Mulgrew, they are the only three absentees. Lustig is out for two to three weeks, it is bone bruising so it could even be longer.
"So I imagine he will miss Juventus. We are hoping Charlie will be fit for Juventus and the game at the weekend.
"Kris [Commons] is back from his virus and Lassad [Nouioui] has had a bit of a virus but he is in the squad."