Nastasic sustained the calf injury in last Sunday’s 6-0 Premier League win over Tottenham.
City boss Manuel Pellegrini has revealed that Nastasic will not feature against Swansea on Sunday.
“Vincent Kompany is fit and he is not ready to play on Sunday but I think next week he will be without any problems,” said the Chilean.
“Jovetic and Silva – I think they will play against Bayern Munich.
“Nastasic needs more time to recover – I think three weeks more.
“Rodwell is fit and can play this Sunday.”