Tests taken on Thursday revealed the prolific striker had suffered anterior cruciate ligament damage in his left knee during Monaco's Coupe de France tie against Monts Or Azergues on Wednesday night and it was announced he would need an operation.
Monaco have not said how long Falcao is likely to be absent for, only that doctors would "make every effort to allow Radamel Falcao to recover as quickly as possible."
However, there must be real concern for Colombia and the player that he will be ruled out of this summer's World Cup finals, with recovery time for a serious ACL injury typically between six and nine months.
Falcao admitted on Twitter on Thursday night that the injury was a devastating blow for him - but at the same time he is not yet ready to accept his chances of making the finals are over completely.
He wrote in Spanish: "I want to thank all of you for so many messages of support in the last few hours, I'm really touched by the warmth that's been shown to me from all over the world.
"I'm not going to deny that my sadness is huge, my heart is broken, but I'm clinging to the smallest hope, and that's enough to think that my World Cup dream is still alive.
"God makes possible the improbable, I believe in Him!!!
Falcao was forced off at half-time of the last-32 cup match against fourth-tier side Monts Or Azergues, after a challenge from Soner Ertek. He had scored the opening goal and Monaco went on to win 3-0.
That took Falcao's tally to 11 goals in 19 matches in all competitions for Monaco this season after joining the big-spending Ligue 1 club in a reported £50million move from Atletico Madrid last summer.
If he is ruled out of the World Cup, the 27-year-old's absence would be a huge blow for Colombia.
He scored nine goals in 13 matches in qualifying - two goals less than top-scorer Luis Suarez of Uruguay - as Colombia booked their spot in Brazil this summer as runners-up to Argentina in the South America section.
Colombia have been drawn alongside Greece, Ivory Coast and Japan in Group C of the World Cup and begin their campaign against the Greeks on June 14.
As news of Falcao's injury spread, messages of support poured in for the former Porto and River Plate striker.
His former colleagues at Atletico wore T-shirts saying "Strength Tigre" (Falcao's nickname) before their Copa del Rey clash with Athletic Bilbao on Thursday night, while his team-mate with Colombia and Monaco, James Rodriguez, tweeted: "Strength and faith brother. We need you, football needs you."
Monaco vice-president Vadim Vasilyev said on his club's website: "All our thoughts and wishes go to Radamel Falcao today. It's terrible news for him and, of course, for AS Monaco FC.
"But we know that such a great player will overcome this setback and return stronger than ever before."
Former England captain Gary Lineker, meanwhile, also rued the possibility that Falcao might not be gracing the World Cup, writing on his Twitter account: "What a terrible blow for Radamel Falcao. One of the game's stars out of the World Cup! Real shame."