He picked up the injury in the first minute of last week’s Champions League draw against Atletico Madrid.
“We are not 100 per cent on the exact timings, but he is certainly going to be out until after Christmas, we think,” said manager Brendan Rodgers.
Hatate will miss 12 games – including three in the Champions League – if he does not return before Christmas while the winter break follows Celtic’s trip to St Mirren on 2 January.
“It’s a disappointment for him. He has had a bit of a broken start to the season and obviously this will take him over the halfway point in the league,” added Rodgers.
“So it is very frustrating for him, especially someone who really commits himself to his game and his professionalism. Everything he does, he tries to do right.”
Hatate had a six-week spell out with a hamstring injury in his other leg towards the end of last season then missed a month with a calf injury earlier this term, so Rodgers is keen to establish if there is a pattern to the muscle injuries.
“It’s just investigating everything he is doing outside of here as well as here and trying to piece it all together,” added the manager.
“It’s a case of trying to look deeper into everything around his development and what he is doing here and what he is doing away from here, just to see if there is anything that we can find out.”
The former Kawasaki Frontale player, who signed a new contract last month that ties him to Celtic until 2028, has won four trophies since being signed by former manager Ange Postecoglou.
Paulo Bernardo filled in for Hatate against Hibernian at the weekend and the Portuguese along with David Turnbull and Tomoki Iwata will likely fill the void alongside Callum McGregor and Matt O’Riley.
Celtic face in-form St Mirren in the Scottish Premiership on Wednesday (19:45 GMT).
