Fellaini limped off after 29 minutes after hurting his left knee in an awkward fall.
While Fellaini was able to leave the stadium without the need for crutches, Martinez sparked concern after revealing fears over ligament damage post-match.
Belgium manager Roberto Martinez hinted that Fellaini's injury is serious and could force him to remain off-field for a long time.
Even though the Belgian ace may have avoided any major cruciate ligament damage, his sprained Medial Collateral Ligament (MCL) will give Mourinho and the Red Devils' fans a major headache. A Belgian FA official also confirmed the injury, and said: "It is something to be anxious about on first sight".
29-year-old Fellaini will undergo an MRI on Sunday, the Belgian FA informed.
Fellaini could also be ruled out of a Champions League away clash at Benfica, before United travel to Huddersfield Town the following Saturday.
A potential added injury to the growing list could not come at a worse time for United, who return after the global break for a crunch fixture with bitter rivals Liverpool.
Fellaini had been deputising for Pogba and he scored twice in the 4-0 win over Crystal Palace last weekend.
Belgium have already qualified for the World Cup next summer and will play a dead rubber against Cyprus on Tuesday.