Pogba has not played since a Champions League win over Basel on 12 September because of a hamstring problem.
Carrick is also injured, while defender Phil Jones can play after a European suspension – but will not feature.
United, unbeaten in eight games this season, and CSKA both won their opening Group A games. While the Red Devils were beating Basel 3-0 at Old Trafford, the Russians won 2-1 away to Benfica in Portugal.
United boss Jose Mourinho said Fellaini’s injury "could have been much worse" but expects the Belgium international to be back in action soon.
"Fellaini was lucky," he added.
Mourinho did not reveal what the injury was to 36-year-old Carrick, who has made just one appearance this season.
"I won’t have Fellaini, I won’t have Pogba, we won’t have Carrick, so all three midfield players that we lose for this match," he said.