Manager Neil Lennon revealed the Sweden right-back had been playing through the pain barrier for several months.
With his country failing to reach the World Cup finals and Celtic out of the Champions League, the decision was taken to undergo surgery.
The 27-year-old has been in impressive form for Celtic but Lennon revealed he had been hampered by the problem.
Lennon said: "Lustig had surgery, four months. He had both hips done, so the procedure was a bit more in-depth than first thought.
"We are hoping he will be back March/April time but he had a lot of work done which makes his recent performances even more remarkable.
"His movement was restricted and he was in a lot of pain after games so it needed doing. So hopefully he will come back an even better player which will be brilliant for us."
Also missing from the Hoops squad for the SPL clash against Hearts at home on Saturday will be Charlie Mulgrew (groin), Dirk Boerrigter (hamstring) and Dylan McGeouch (knock).
James Forrest trained after recovering from a hamstring complaint as did Tom Rogic, who had been out with a calf injury while Beram Kayal (foot) and Steven Mouyokolo (Achilles) remain out.
Gary Locke's Hearts squad is once again stretched to the limits.
The administration-hit Gorgie club - barred from signing new players - have lost striker Gary Oliver to a leg injury and he joins Ryan Stevenson (hamstring), back-up goalkeeper Mark Ridgers (knee) and midfielder Jason Holt (foot) on the sidelines.
To add to Locke's woes, midfielders Jamie Walker and Scott Robinson are rated as doubtful.