The City midfielder limped off after just 12 minutes as La Roja drew 1-1 with France in Madrid on Tuesday.
“We have a lot of injury problems after the international break,” Mancini revealed.
“David has a hamstring problem and is not ready for tomorrow.
“We hope that he will be ready for the next Premier League game against Swansea.”
Javi Garcia and Jack Rodwell are also carrying injures and will not feature tomorrow.
“Javi I think will be out for another week maybe, Jack is out too,” Mancini confirmed.
The City boss also expressed concern over the England internationals who he says are “tired,” after their game against Poland in Warsaw was put back a day due to a waterlogged pitch.
“I think that sometimes when we have this situation, we can move our game from Saturday to Sunday if it is possible. We play at 3 o’clock on Saturday,” stressed Mancini.
“I am not disappointed, but I am worried because today the players – Joe, James and Joleon – it’s the first training together and tomorrow we play, but we can’t change it now.”