The Spaniard sustained the problem in the first leg draw at the Etihad, a game in which Pellegrini felt his side played ‘very well’.
Playmaker Silva limped off before half-time – something which Pellegrini feels disrupted his side’s performance – and the Chilean does not expect the 30-year-old to feature at the Bernabeu next Wednesday.
“He has a hamstring (injury),” Pellegrini confirmed to BT Sport.
“I don’t think he will be fit in one week.”
On the performance, he said: “We defended very well, we tried to create until David [Silva] was injured, after that we lost the ball too much and did not create clear chances.
“We play very well away, we beat Sevilla, drew against Paris St Germain.
“We will go to the Bernabeu and there will be more space, Real Madrid must attack a little bit more.”
Captain Vincent Kompany, who returned after missing the weekend win over Stoke, says the Citizens are ready for ‘a rumble’ in the Spanish capital.
“Nil-nil is a very dangerous score,” Kompany admitted.
“From the moment we manage to score in Madrid, it will be a very different game.
“It’s a good result, it’s hard to keep a clean sheet against a good attacking team. We can be proud of what we’ve achieved in the first leg.
“[Joe Hart] had to pull off a few saves, mainly on set-pieces so we need to look at that next time and make sure that doesn’t happen.”