Dutch boss Guus Hiddink fears the problem could rule him out for a number of weeks, which would leave United boss Louis van Gaal with a selection crisis.
The midfielder was forced off after 20 minutes in Amsterdam during his side's Euro 2016 qualifier following a challenge by Eduards Visnakovs.
Speaking after the victory, Hiddink spoke of his concern for the 24-year-old, who limped off rather than leaving on a stretcher.
"It doesn't look good," he said. "It's his medial ligament.
"It could be a strain, but it could also be a tear. So that's a big blow,"
Van Gaal will hope Hiddink's assessment is a cautious one, and he will receive good news ahead of the Premier League clash with Arsenal next weekend.
His absence would see United's options depleted even further, with a host of players already on the sidelines, including a number of defenders.
Van Gaal is also hoping goalkeeper David De Gea will recover from a dislocated finger in time to face Arsene Wenger's men at the Emirates Stadium.
