In a statement the club revealed their star forward had suffered "an anterior cruciate ligament strain".
It added: "Surgery is required. The doctors will do everything possible to enable Radamel Falcao to recover as quickly as possible."
Falcao faces a lengthy spell on the sidelines, and although the club did not specify how long they expected him to be out of action the news will raise concern over his FIFA World Cup™ participation.
On Wednesday, Falcao crumbled to the ground following a challenge and needed lengthy treatment before being carried away on a stretcher just before the interval in his club's 3-0 victory at Chasselay.