The Danish player had to be substituted during United's 3-1 win over Reading on Saturday in the FA Cup following a foul by Andy Carroll and a statement from the club on Tuesday said he was "likely to be out until late April or early May".
Eriksen, who needed life-saving treatment on the pitch in June 2021 after suffering a near-fatal cardiac arrest in a European Championship match against the Finns, has been instrumental in United's impressive form this term.
He has played 31 of United's 32 matches in all competitions this season, scoring two goals and providing nine assists.
The midfielder joined United last year after leaving fellow Premier League side Brentford, where he had re-established his career on a short-term deal after his heart problems.
"We are disappointed about it but it happens in top football," United manager Erik ten Hag said on Tuesday.
"We have to deal with it. We have good players in the midfield department but I think we can never fill that because every player has his own characteristics.
"Cristian Eriksen brings top quality and especially in some specifics that is hard to replace. His impact in the final third."
Speaking ahead of Wednesday's League Cup semi-final, second leg at home to Nottingham Forest, Ten Hag said it would be difficult to sign a replacement on transfer deadline day.
United are 3-0 up from the first leg.
