Manchester United say that both Zlatan Ibrahimovic and Marcos Rojo sustained “significant knee ligament damage” in the win over Anderlecht on Thursday.
Ibrahimovic had been expected to miss the remainder of the season, according to Sky sources, and such an injury would suggest Rojo's campaign is also over with just five weeks remaining in the season.
United did not give a specific timeline for recovery and said that both players will see specialists in the coming days.
Both players had to be taken off in United's 2-1 Europa League quarter final win over the Belgian side on Thursday, with Ibrahimovic's knee buckling as he landed awkwardly just before the end of normal time while Rojo was taken off on a stretcher after just 23 minutes.
A United statement said: "Detailed investigations on the injuries sustained by Marcos Rojo and Zlatan Ibrahimovic during Thursday's Europa League match have confirmed significant knee ligament damage in both players that requires specialist opinions over the coming days.
"Estimations of time to full recovery will only be possible once definitive treatment plans have been decided after these consultations."
Ibrahimovic, who has scored 28 goals for United this season, is out of contract in the summer and has yet to agree an extension to remain at the club for another year.
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LA Galaxy are reportedly interested in the striker, who arrived at Old Trafford last summer on a free transfer from Paris Saint-Germain.
Rojo's injury leaves United short in defence, with Chris Smalling and Phil Jones still on the sidelines.
His absence means that Eric Bailly and Daley Blind are United's only fully fit centre halves going into the Super Sunday trip to Burnley, live on Sky Sports 1.
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