The Times says the Armenian aggravated a thigh injury in the 2-1 defeat to Manchester City on Saturday.
He was taken off at half time after a disappointing first half but this news suggests it wasn't just his performance that caused Jose Mourinho to make a change.
Mkhitaryan joined United early in the summer for a fee of around £28m from Borussia Dortmund.
However, he has had a frustrating start to his Old Trafford career and isn't happy with the position Mourinho is playing him.
The 27-year-old has appeared in all of United's games so far this season but his only start so far was against City.