The 25-year-old Frenchman won't need surgery after he sprained his knee against Kazakhstan last week in a World Cup qualifying match and believes he will return before the Euro 2020 tournament this summer.
Manchester United manager Ole Gunnar Solskjaer was not at optimistic on Martial's diagnosis, saying on Sunday that the player is likely to miss the rest of the season.
"Unfortunately, he sprained his knee with France," Solskjaer told MUTV. "It's always when they go away on internationals... you can keep your fingers crossed and hope they come back fit.
"Losing Anthony for what might be the rest of the season is very disappointing, especially when reports from there [France] was that it wasn't anything serious but it looks a bad one."
Martial has scored seven goals for United this season but has just three in 19 appearances in 2021.