After the Ligue 1 outfit confirmed on their official website that the forward will undergo an operation, the Colombian is expected to miss the World Cup in Brazil this summer.
A statement read: "Following the injury suffered on Wednesday, Radamel Falcao has undergone medical examinations. It appears that the player has an injury of the anterior cruciate ligament in his left knee.
"Surgery is necessary in the coming days. Doctors will therefore make every effort to allow Radamel Falcao to recover as quickly as possible."
Falcao has netted nine goals in 17 league games for Monaco so far this season.