The 29-year-old Chilean forward, dropped from the squad for Tuesday's 1-0 Champions League win over Swiss outfit Young Boys, suffered the injury in training on Thursday.
Alexis Sanchez's miserable spell at Manchester United took another turn for the worse on Friday with manager Jose Mourinho announcing he faces several weeks out with a hamstring injury.
"It is an aggressive muscular injury," Mourinho said at Friday's press conference.
"He has not had a scan yet but the player is experienced. He knows what injury is.
"From my experience, the painful scream and way it happened, it will be a long time.
"It is not a little muscular injury that he will be ready in a week or 10 days.
"For me and Alexis Sanchez, the grade is different to the one that Lindelof (expected to miss three weeks due to a thigh strain suffered against Crystal Palace last weekend) has and that was not easy."
Sanchez's first team starts have been rare in November, and he came on as a substitute in the league games against Manchester City and Crystal Palace. He last started in the victory at Juventus in the Champions League on November 7.