The Colombian crumbled to the ground following a challenge by Soner Ertek inside the Chasselay area -- for which no penalty was given -- just before the interval and needed lengthy treatment before being carried away on a stretcher underneath a blanket.
He had given the Principality club the lead just before the half-hour mark, tapping into an empty net after Valere Germain had headed down a cross, his 11th goal in French football setting Monaco on their way to clinching a place in the last 16.
Emmanuel Riviere replaced the former Atletico Madrid striker after half-time and went on to score two more goals in a game that was played at Lyon's Stade de Gerland.
The injury to Falcao and the fall-out from it somewhat marred what should have been a special occasion for fourth-tier strugglers Chasselay and their star player, veteran former Monaco captain Ludovic Giuly.
"When you play against a team from a lower division, they are going to play really hard," Monaco coach Claudio Ranieri said. "That's normal, and that is what I tell my players before the match but it's not possible for a referee to blow his whistle for free-kicks without ever booking anyone."
"If Falcao has something serious, it is the referee's fault.
"Everyone wants to play like in England and let the game go. It's not possible here. The referee must see when there is a foul and blow his whistle."
Meanwhile, Monaco released a statement in which they said: "The player Radamel Falcao was hit in the left knee. Must await further tests in the coming days to clarify the exact nature of the injury."
Ertek himself admitted to being upset at the potential implications of his challenge.
"I am gutted. I honestly don't think I touched him," he said.
"Did he hurt his own ankle? Did I touch him accidentally? I don't know but it ruined my match."