The teenager came off worse in challenge with Saliou Ciss after 66 minutes on Friday night and is expected to be sidelined for at least three weeks.
Martial looks set to miss the Coupe de France clash at Vannes on January 5 and the first league game after the mid-season break against Montpellier five days later, but head coach Claudio Ranieri will hope to welcome him back for the trip to Toulouse on January 19.
The 18-year-old's injury was tempered by the fact that the Principality club's record signing Radamel Falcao was able to make his return as a substitute after a lay-off of almost a month due to a thigh problem.
Monaco's 2-1 shock defeat at Stade Louis II ensured they are three points behind leaders Paris Saint-Germain, who were held to a 2-2 draw by Lille on Sunday.
