Falcao sustained an ankle injury during the match against Marseille and is now in doubt to play the WC Qualifiers this week.
Monaco moved back to the top of Ligue 1 as they ended Marseille's unbeaten record with a 2-1 win at the Stade Velodrome on Sunday.
Monaco are still yet to taste defeat since earning promotion from Ligue 2 last season, but paid a heavy price for their win as star striker Radamel Falcao suffered an ankle injury in the second half and is now in doubt for the upcoming WCQ to be played on Friday and next Tuesday.
Marseille went in front just a minute before the interval as Lucas Mendes headed in Mathieu Valbuena's corner. However, their advantage did not last long, Falcao equalizing early in the second period with his third goal of the season.
The Colombian did not finish the match, but his replacement Emmanuel Riviere scored the winner with his fifth of the campaign. Riviere - signed from Toulouse in January - slotted home after latching on to a superb through-ball from Joao Moutinho.