The 26-year-old, on loan from Queens Park Rangers, sustained the injury to his right knee during Tuesday's Champions League clash with Shakhtar Donetsk, who won 2-0.
Real Sociedad released an official statement on their club website confirming the news of the injury.
"The MRI scan done this morning discovered a ruptured anterior cruciate ligament and medial meniscus injury in Granero's right knee," read the statement.
"This injury will require surgical repair. The player will perform a physical therapy focused on stimulating and maintaining the neuromuscular control of the joint."