The Colombia international opened the scoring just before the half-hour mark but was left holding his left leg in a crumpled heap after a heavy challenge four minutes before the break.
Falcao immediately called for medical attention and was stretched from the field, grimacing in pain.
The severity of the damage to the striker's left knee has yet to be established but any lengthy lay-off would be a major blow for Monaco, who are currently second in Ligue 1, five points behind leaders Paris Saint-Germain.
Colombia will also have grave concerns about their star striker missing this summer's World Cup in Brazil.
Falcao made a fine start to life in Ligue 1, after joining Monaco from Atletico Madrid last summer, but has struggled with injuries and loss of form in recent weeks, while there has also been talk of a falling out with Les Rouge et Blanc boss Claudio Ranieri.
