The Swedish internationalist, one of the most consistent performers for the Scottish champions this season, will be out of action for around two months.
It is the last thing Hoops manager Neil Lennon wants as he wrestles with a growing injury list. Derk Boerrigter (hamstring), Beram Kayal (ankle), Steven Mouyokolo (Achilles), Charlie Mulgrew (groin) and Tom Rogic (calf) are all unavailable just now.
There is also speculation that Joe Ledley and Georgios Samaras, who have failed to agree extensions to their current deals, may leave the Parkhead club next month.
Both are believed to be on the radar or Barclays Premier League clubs Cardiff City and Hull City and could depart in the January window.
Lennon is hopeful that winger James Forrest, who has been struggling with a back problem, will be able to return to training at Lennoxtown at some stage this week.
However, losing right-back Lustig is still a setback for the Celtic boss as he attempts to extend his side's impressive 15-game unbeaten run in the SPFL Premiership.
The Irishman is particularly concerned about the centre-half position, where he is short of back-up for first-choice duo Virgil van Dijk and Efe Ambrose. He said: "The squad is really thin with Boerrigter, Mulgrew, Kayal and Rogic all out just now. I need cover at centre-half.
"If anything happens to the two boys who are in the team then I am in trouble. Lustig is going in for surgery on Thursday so we are going to be missing him for a couple of months at least."
Lennon was deeply disappointed that Celtic failed to book a place in the knockout stages of the Champions League for the second season running.
But he believes not being involved in Europe may benefit of his threadbare squad as they bid to land a SPFL Premiership and Scottish Cup double.
He said: "Now that the Champions League is out of the way, that might spare us a game or two here and there.
"Physically and mentally, we will have a little bit more rest between games so hopefully that will help us."