Hoeger, 24, who is due to have surgery, sustained the injury in the 3-2 weekend win over Eintracht Braunschweig.
He joins a growing list of injured players as Schalke prepare to host Chelsea in the Champions League on Tuesday.
"The Royal Blues will likely have to be without him until the end of the season," Schalke said in a statement.
The Bundesliga club are already without striker Klaas-Jan Huntelaar, who underwent further knee surgery earlier on Monday and is not expected to return until after the winter break, and defender Kyriakos Papadopoulos.
Midfielder Jefferson Farfan will also miss Tuesday's game.
"The situation is obviously far from ideal," coach Jens Keller told a news conference on Monday. "But with Jermaine Jones, Kevin Prince Boateng and (keeper) Timo Hildebrand we have players coming back who can help us.
"We have to accept this situation and not complain. We have already shown with these players what we are capable of."
Boateng, who has helped Schalke bounce back from a bad league start after joining from AC Milan in September, will train on Monday after missing the Braunschweig game with a nagging knee injury.
"He will train today. He has done some individual sessions and we all hope the knee will hold. We want to win the game and crown it with the three points," Keller said. "We are going into this match to win it."
Teenagers Leon Goretzka and Max Meyer, who both scored at the weekend, are again expected to be in the squad.
"Max is obviously a huge talent and he has undergone a development explosion in the past few weeks," said team mate Julian Draxler.
"He is extremely important for us just like all the young players in the team."
Schalke top Group E with two wins out of two with Chelsea in third on three points, the same as Basel. Steaua Bucharest have yet to pick up a point.
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- Kyriakos Papadopoulos
- Eintracht Braunschweig