The Spain playmaker felt discomfort in the closing stages of last Sunday's victory over West Ham, a game in which Silva scored the Premier League leaders' late winner.
City announced on Monday that Silva would not be travelling to Kharkiv for City's Champions League game against Shakhtar Donetsk on Wednesday because he was "not fully fit".
It was assumed this was a precautionary measure but manager Pep Guardiola has now revealed the 31-year-old, who signed a contract extension last week, is also in danger of missing the trip to Old Trafford.
Guardiola, speaking at his pre-match press conference in Ukraine, said: "David had a little bit of problems in the last minutes. We made a test after the game and I don't know if he is able to play on Sunday, so that's why he stayed there, to recover in Manchester."
Guardiola was asked for further clarification on the nature of the injury but was unwilling to elaborate.
He said: "It's something, something uncomfortable he felt in the last minutes, before the goal he felt something."
After being asked again, Guardiola laughed and said: "Hopefully he can be fit for Sunday but it was too risky to play him (Wednesday)."