A crunching challenge from Andy Carroll which earned the Reading striker a red card in Saturday's FA Cup tie at Old Trafford has caused significant damage.
United won the game 3-1 to advance to the fifth round of the FA Cup.
Eriksen has made a significant contribution to Manchester United's resurgence under Erik Ten this season, making 31 appearances across all competitions and adding two goals and nine assists.
The 30-year-old moved to Old Trafford on a free transfer in the summer, signing a three-year contract.
A statement read: "Manchester United midfielder Christian Eriksen is expected to be out of action for an extended period because of an ankle injury sustained in our Emirates 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."
Reacting to the news, manager Ten Hag said: "He's disappointed and we're disappointed, but it happens in top football. You have to deal with it."
"We have players in midfield, good players, who can fill the gap. Every player has their own characteristics and identity. Eriksen brings top quality to our squad and some characteristics are hard to replace, for instance his quality in the final third."
Manchester United begin a lengthy string of games without Eriksen on Wednesday when they take on Nottingham Forest in the Carabao Cup semi-final second leg.
The Red Devils lead 3-0 from the first leg.
