United have confirmed Fernandes suffered a soft tissue injury in the first half at Villa Park. The Portugal international appeared to hurt his hamstring but played on until half-time before being replaced by Lisandro Martinez at the break. He was later seen walking uncomfortably along the touchline.
"I think it's soft tissues, so it's going to take a while. We'll see," Amorim said. "During this year, especially in this time, we have so many problems, but we have to cope with that."
Fernandes' injury added to United's growing list of absentees. Bryan Mbeumo, Amad Diallo and Noussair Mazraoui are all away at the Africa Cup of Nations, while midfielder Kobbie Mainoo was ruled out after suffering a calf injury in training.
"He is going to be fine in a few weeks, I think, I don't know," Amorim said of Mainoo. "Let's focus on the players that we have and are ready to play."
Villa secured the win through two goals from Morgan Rogers, but Amorim felt his side had done enough to take something from the game despite being forced into a midfield reshuffle after Fernandes went off.
"I think we were the better team today. We were unlucky, even with the injury of Bruno," Amorim said. "We did a very good job that no one is going to remember tomorrow, because what matters is the result."
Amorim handed debuts to Shea Lacey and Jack Fletcher, the son of former United midfielder Darren Fletcher, as United looked for solutions from the bench.
Defender Diogo Dalot admitted Fernandes' potential absence would be a major setback.
"It's massive," Dalot said. "We don't know how bad it is, but for him to come off, we know how tough he is. This is the time other players have to step up. We are Manchester United, and we have to find a way to win."
United are seventh in the Premier League on 26 points, ten behind third-placed Aston Villa.
Mikel Arteta said Arsenal won because his players stayed fully focused on the single task of beating Everton on Saturday, insisting that discipline and concentration were the key reasons they returned to the top of the Premier League.
Pep Guardiola has said his Manchester City players will be weighed when they return to training to make sure they are fit enough to face Nottingham Forest on 27 December.
Egypt captain Mohamed Salah has put his recent troubles at Liverpool behind him and is fully focused on winning the CAF Africa Cup of Nations, according to national coach Hossam Hassan.
Manchester United suffered yet another blow to their Premier League campaign with a 2-1 defeat to an in-form Aston Villa at Villa Park on Sunday evening.
