Falcao, who grabbed the opening goal for Monaco, was scythed down shortly before half-time and looked in serious discomfort as he was carried off. Monaco went on to win 3-0.
"We lose Radamel Falcao. It's a big blow. I think it is serious. The news is not reassuring," captain Jeremy Toulalan told Eurosport.
Monaco issued a statement following the match, though it gave away no detail other than what was already fairly clear: "Radamel Falcao was hit in the left knee. We must wait for further tests in the coming days to clarify the exact nature of the injury."
The Colombian was joint third top scorer during World Cup qualifying, scoring nine goals, and his country now faces an anxious wait while the severity of the injury is established.
Brazil's showpiece tournament is less than five months away, and should the striker have sustained a broken leg or ACL injury he might be ruled out of contention.
A lengthy absence would also be a huge blow to Monaco’s hopes of reeling in Paris Saint-Germain at the top of Ligue 1.