United expect Eriksen to be ruled out until late April, but there remains hope he might play again this season.
The club said in a statement on Tuesday: "Christian Eriksen is expected to be out of action for an extended period because of an ankle injury sustained in our FA Cup victory over Reading on Saturday.
"While investigations are continuing, initial assessments indicate that Eriksen is likely to be out until late April or early May.
"However, there is hope that Christian can return in time to play a role in the final stages of the season."
Eriksen's injury is a blow to manager Erik ten Hag, who is already without midfielder Donny van de Beek. The midfielder has been ruled out until the summer with a knee injury.
"He's disappointed, we are disappointed, but it happens in top football and you have to deal with it," Ten Hag told a news conference on Tuesday. "I think you can never fill that [gap] because every player has his own characteristics, identification. Another player will always fill in in a different way, but it doesn't mean you have to be less successful.
"It's quite clear Christian Eriksen brings top quality to our squad and he has some specifics that are hard to replace, such as his impacts in the final third with his final ball."