The 35-year-old Ibrahimovic sustained damage to his right knee late in the game against Anderlecht on Thursday and was assessed by the club's medical staff.
He looks certain to miss the rest of the season as United battle to finish in the Premier League's top four and win the Europa League. They play Spanish side Celta Vigo in the semi-finals of Europe's second-tier club competition.
United did not issue any update on his condition but ligament damage could rule him out until the end of the year.
Ibrahimovic, United's leading scorer this season with 28 goals, is out of contract at the end of the season but has been talking to the club about a 12-month extension.
He has been linked in media reports with a move to Los Angeles Galaxy or Los Angeles FC.