Celtic midfielder Hatate sidelined two months with hamstring injury
Tests have revealed significant damage that will keep the Japan international sidelined for the next 12 games after leaving the pitch injured in the opening minutes of last week's Group E clash against Atletico.
"We are not 100% on the exact timings, but he is certainly going to be out until after Christmas, we think," said Rodgers.
"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.
"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, who last month signed a contract extension with Celtic until 2028, also missed six weeks last season with the same injury to his other leg, and was out a month with a calf injury earlier this campaign.
Celtic play St Mirren in the Scottish Premiership on Wednesday. They face the same opponent on January 2nd, when Hatate could return to action.