The defensive midfielder limped off in the 51st minute of the 2-0 win against United at Old Trafford and could be a doubt for Sunday's game at Burnley.
"We will see tomorrow. We are going to make the scan and we will see. I will talk to the doctor and he will make the best decision for everybody," Fernandinho said.
"When I blocked the shot from Paul (Pogba) I felt my knee. It twisted a little bit. I could continue playing but I came off. That's what it is," he said.
City already have key midfielder Kevin De Bruyne sidelined with a hamstring injury he picked up in Saturday's win over Tottenham Hotspur.
Pep Guardiola's side are a point clear of Liverpool at the top of the table, with three games remaining.
(Reporting by Simon Evans; Editing by Toby Davis)
