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.
"Lustig had surgery and will be out for four months," said Lennon. "He had both hips done.
"The procedure was a bit more in-depth than first thought. We are hoping he will be back around March-April time.
"He had a lot of work done so it makes his recent performances even more remarkable really. His movement was restricted and he was in a lot of pain after games so it needed doing.
"Hopefully he will come back an even better player which would be brilliant for us."
Lennon will also be without injured quintet Charlie Mulgrew, Dylan McGeouch, Steven Mouyokolo, Derk Boerrigter, Baram Kayal for Saturday's Scottish Premiership meeting with Hearts.
With Celtic seven points clear at the summit, Lennon intends on rotating his squad during the busy Christmas period.
"The tournament is academic," said the Northern Irishman. "We will use it as a training game more than anything else.
"We have a really heavy schedule from the middle of July right through to end of this month so opportunity there to take some time off and take players away.
"We found the benefit of it last year and feel this year will be no different."
Meanwhile, Lennon had no update regarding the futures of Georgios Samaras and Joe Ledley.
The duo's contracts expire next summer and Lennon is keen to keep them at the club.
"The ball is very much in their court," said Lennon. "It's getting to the point where will be a lot of speculation.
"Their contracts are up in the summer and they are two players we don't want to go but we can't force them to stay.
"We are doing everything we can at the minute to do that. We have had no indication either way of what the players want to do."