The France international will be out of action for up to three months, after he left the field early during his side's Ligue 1 win on Saturday
The 26-year-old was forced to leave the pitch after only 12 minutes of play due to the knock, and underwent further examination on Monday to determine the full extent of the injury.
Club doctor Robert Duverne has now revealed that Gourcuff has sustained ligament damage and will be out of action for up to three months.
"At the time it happened, I feared he had torn his cruciate ligaments. His ankle didn't move along and his leg just seemed to lock itself," Duverne stated to Le Progres.
"It is not as bad as expected, as he has sprained his right knee and damaged his lateral collateral ligaments, but it's a serious injury. He could be out for anything between six to 12 weeks."
Lyon currently top the Ligue 1 table with six points from two games.