The 24-year-old sustained the injury to his right knee during Saturday's 3-2 Bundesliga win at Eintracht Braunschweig and underwent surgery on Monday afternoon.
Hoger, a mainstay in the Royal Blues' midfield since the end of August, joins Klaas Jan Huntelaar in the treatment room with a similar injury. The Holland striker went under the knife at a clinic in Augsburg on Monday morning.
Huntelaar is expected to be back in action in January, although Hoger faces a six-month lay-off.
Furthermore, Kevin-Prince Boateng and Jermaine Jones are also labouring with knee niggles which ruled them out of the weekend game.
The Gelsenkirchen club host Chelsea in the Champions League on Tuesday evening.