The Colombia international was taken from the field on a stretcher in Monaco's 3-0 triumph over Monts d'Or Azergues in the Coupe de France on Wednesday.
Monaco confirmed on Thursday that their record signing will undergo surgery after scans revealed he had damaged the anterior cruciate in his left knee, with the 27-year-old's hopes of playing at the World Cup in Brazil later this year seemingly over.
But Falcao is retaining hope of appearing at the elite tournament.
"I want to thank all of you for your messages in the last hours," he wrote on social networking site Twitter.
"I have been touched by all the support and love of all the people around the world.
"I am not going to hide that I am very sad. My heart is destroyed. But I have faith (that I am) holding right now to keep my dream alive to be at the World Cup.
"God makes the impossible possible. I believe in Him."
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