The France international underwent the scans on Wednesday after he limped out of the Champions League victory over Basle on Tuesday night with the problem.
United have yet to make any comment and may leave it until Jose Mourinho addresses to media on Friday, but reports claim Pogba will be out for six weeks.
If that is the case he will miss the Premier League fixture against Everton on Sunday along with the games against Southampton and Crystal Palace.
The Carabao Cup tie against Burton on September 20 and the match against CSKA Moscow in the Champions League on September 27 are also a no go, along with United's clash with Liverpool at Anfield on October 14.
Speaking after the Basle win, Mourinho said United have enough quality and strength in depth to cope with any spell on the sidelines, but the loss of Pogba, who has been a revelation so far this season, is a big blow nonetheless.