The Spaniard has been ruled out for two to three weeks after limping out of Tuesday's scoreless first leg.
Silva, 30, would be fit for the final on 28 May, should City get there.
Midfielder Yaya Toure, who missed the first leg because of a thigh injury, returned to training on Friday and will be assessed before the game in Madrid.
City, who are third in the Premier League, travel to eighth-placed Southampton on Sunday, kick-off 16:30 BST.
They wanted the match to be brought forward a day to give them extra time to prepare for Wednesday's match.
The Premier League rejected an initial enquiry by the club, and boss Manuel Pellegrini is unhappy Real will have more than 24 hours' extra rest.
Their league game this weekend - at Real Sociedad - kicks off at 15:00 BST on Saturday.
"I don't understand why we cannot play one day before," said Pellegrini. "Why can't we at least be in the same situation as Real Madrid?
"We are representing Manchester City but we are also representing England in the Champions League. You don't want to give advantage to the other team."
Manchester City midfielder David Silva will miss Wednesday's Champions League semi-final second leg at Real Madrid because of a hamstring injury.