The 27-year-old, one the world's top strikers, underwent surgery this weekend in Portugal by a team led by Jose Carlos Noronha, who was cautious about predicting Falcao's chances of making the World Cup earlier in the week.
Monaco did not elaborate on the length of Falcao's absence, while media reports suggested he could be out for six months.
But Noronha told reporters at the hospital in Porto that not only was the operation a success, but "it is not out of the question" that Falcao can make it back in time for the showcase international tournament.
Noronha was quoted by the Associated Press as saying the forward "has a better than 50 per cent chance" of being involved at the World Cup.
The tournament in Brazil kicks off on June 12, less than five months from now.