Fellaini was forced off after 29 minutes of Belgium’s 4-3 World Cup qualifying win over Bosnia-Herzegovina on Saturday.
Head coach Roberto Martinez admitted it was likely the midfielder had damaged a ligament and there had been concerns he had suffered a tear.
However, tests have revealed he has only sprained the medial collateral ligament of his left knee and is likely only to be out of action until the latter part of the month, with Belgium confirming the news via their official Twitter account.
It is a blow nonetheless for United, who must take on fierce rivals Liverpool in the next Premier League match without Fellaini or Paul Pogba in central midfield.
The 29-year-old has scored four goals in all competitions for the club in a resurgent run of form this season, prompting speculation he will be offered a two-year extension to his contract, which expires in 2018.