The striker was a notable absentee for Thursday night's Europa League clash with Club Brugge.
Before the European contest, United boss Ole Gunnar Solskjaer told MUTV: "He didn't feel right after training yesterday, or he walked off during training. He's injured.
"So hopefully it won't be too bad but I don't really know yet how long he'll be [out for]."
As a result, the 24-year-old has emerged as a doubt for Sunday's clash with Everton, where the 20-time English champions will be looking for their third straight Premier League success.
Martial has scored 15 times in 31 appearances at club level this season, including three goals in his last three appearances against Chelsea, Brugge and Watford. body check tags ::