The Colombian striker picked up the injury, which could potentially see him miss this year's World Cup in Brazil, during Monaco's recent fixture in the Coupe de France.
"They didn't give a percentage to my chances of making the World Cup, but they said I have a small chance," said Falcao, according to Ligue1.com.
"That chance is something for me to cling onto. But you have to take these things one step at a time. It's going to be a long battle.
"What I needed to cry about, I've cried about. Now my spirits are high, I'm full of conviction and determined to recover as quickly as possible."
Monaco currently find themselves in second place in the Ligue 1 table.