Silva scored City’s winner in the 2-1 victory over West Ham at the weekend.
But he has been ruled of Wednesday’s Champions League trip to Shakhtar Donetsk.
And, in a big blow for Pep Guardiola, the Spaniard will also likely miss the derby.
“David had problems in the last minutes (against West Ham). We had a test after the game,” Guardiola said in his press conference today.
“I don’t know if he’ll be able to play Sunday. He stayed to recover in Manchester.”
Guardiola then evaded giving details of Silva’s injury.
“He was uncomfortable before the goal, he felt something,” he added.
“Now hopefully he will be fit for Sunday – but it was too risky to play here.”
City have scored late to claim wins in each of their last four outings.
Silva’s 83rd-minute volley helped the Premier League leaders edge past West Ham on Sunday.
City are already into the knockout stage of this season’s Champions League, having won all five of their group games so far.
United themselves will already be without Paul Pogba for the derby at Old Trafford after he was sent off in their 3-1 win against Arsenal.
Pogba was shown a straight red for a stamp on Hector Bellerin but will play CSKA Moscow in tonight’s Champions League outing.