SFR Sport's Johnny Severin relayed the news and more details of the problem picked up by the Frenchman, with the player carrying a "slight thigh injury."
Martial has been utilized often by manager Jose Mourinho this season, with the French national making 38 appearances across all competitions, including 26 in the league, where he has scored nine goals and added five assists.
Without Martial, United do have options to come in on the left flank, with Jesse Lingard perhaps the most natural fit for the role.
Additionally, Marcus Rashford has shown a versatility in where he can be used along the front line, but Alexis Sanchez is expected to remain first choice for the Red Devils.
Questions about the massive fee United paid to sign Martial in the summer of 2015 faded away, as the attacker took to life in the Premier League tremendously in his debut term at the club.
The former Monaco man excelled from a wide position on the left flank, with his blistering pace and wonderful close control so difficult for defenders to deal with. A haul of 18 goals in his debut term points to a player who knows where the back of the net is.
But his second season didn't meet expectations as he tallied just eight goals and eight assists in all competitions. Martial will be keen to return and continue to add to his 11 goals and 10 assists this campaign.
With Martial's pace, power and composed finishing impressive for a footballer who's still so young, United supporters will be disappointed to see him sidelined.