"AS Monaco is saddened by the withdrawal of Radamel Falcao for the World Cup.
"Unfortunately, we have to accept the judgement of the medical expects that he isn't yet ready to play in such a demanding competition as the World Cup.
"Radamel has worked very hard since his injury and had hoped to take part in this adventure. AS Monaco has supported him every step of the way.
"Now our aim is to help him get back to his very best for the upcoming season.
"We also wish every success to the Colombian national team and our player James Rodriguez in this competition."
Left out of José Pékerman's 23-man squad for the competition, Radamel Falcao will play no part in the 2014 FIFA World Cup in Brazil. Scorer of 20 in 51 caps, El Tigre - who underwent left knee reconstructive surgery in January - had been training with the Colombian national team since late May, but his recovery was not judged sufficient by the national team's medical staff to play in the World Cup.