A resurgent Fellaini has scored three Premier League goals this season, as well as netting in the Champions League defeat of Basel at Old Trafford, after stepping up in the absence of the injured Paul Pogba.
But the midfielder was replaced in the 29th minute of Belgium's match in Sarajevo after going down with an injury sustained to his left knee.
Belgium manager Roberto Martínez said after the match that he was fearful that the midfielder has suffered a knee ligament injury.
"We are all worried about Fellaini," Martinez was quoted as saying by Sky Sports.
"We fear that there is ligament damage."
An official from the Royal Belgian Football Association added: "It is something to be worried about on first sight. Ligaments, left knee. More news [on Sunday]."
And with Michael Carrick struggling to shake off a knock that has kept him out of Premier League action all season, Jose Mourinho's midfield options are likely to be severely restricted for the trip to Anfield on October 14.
Ander Herrera looks set to partner Nemanja Matic in midfield, with Daley Blind and Juan Mata among the other alternatives to play in the middle of the park.
Romelu Lukaku also missed Belgium's match against Bosnia-Herzegovina, with the on-form striker unavailable for Roberto Martinez's side due to an ankle problem.
United are only behind rivals Manchester City on goal difference at the top of the Premier League, both sides having taken 19 points from their first seven fixtures.
Belgium were 1-0 up at the time of the 29-year-old's substitution, with a thrilling match eventually ending 4-3 in the favour of Martinez's men, who had already booked their place at the tournament in Russia.