The club said both players are set to see specialists before treatment and recovery plans are decided.
Swedish star Ibrahimovic scored 28 goals in his first season in English football while Rojo has established himself as a first-choice centre back under Jose Mourinho.
Ibrahimovic suffered the injury during Manchester United's 2-1 victory over Anderlecht in the Europa League. As for Ibrahimovic, who has yet to extend his deal with United beyond the end of the season, there are concerns that the injury could be enough to bring to an end his time with the club entirely - not just his season.
"I will rotate players again (on Thursday), give rest to some players again and let's see what we can do".
Manchester United striker Zlatan Ibrahimovic faces a long injury layoff after landing awkwardly on his knee in the Europa League quarter-final win over Anderlecht, British media reported on Friday.
Around the same time, ESPN FC's Jeff Carlisle and Doug McIntyre reported that Ibrahimovic was in discussions to play in MLS.
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JOSE MOURINHO has refused to rule out that Zlatan Ibrahimovic's playing career is over. "When their chance comes, they take it and the team at the moment are very strong in training and everyone is fighting for a place because we have important games coming up".
Breaking news - Zlatan expected to miss remainder of season because of knee injury.
"We knew this would be a hard place to come to and win", said the 31-year-old, before admitting there had been a clear game plan to combat Burnley's style, a plan which was executed to a tee.
The United striker hit the winning goal after 107 minutes at Old Trafford to follow up his earlier assist for Henrikh Mkhitaryan's opener, Sofiane Hanni's first-half strike for the visitors having ultimately forced extra time.
Mourinho compared the situation to Rashford being selected for United's under-23 team to win "say a derby against Manchester City".
Mourinho said both players would be able to come back sooner than anticipated if they put their minds to it.
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