The 32-year-old defender, who has 37 Argentina
caps, joined from Atletico Madrid in a £4.2m deal
on Sunday.
While the centre-half does not need surgery, his
loss adds to manager Manuel Pellegrini's defensive
problems.
Captain Vincent Kompany is expected to be
sidelined for another three weeks with a groin
injury, while Micah Richards has a hamstring
strain.
Demichelis had only joined previous club Atletico
Madrid in July after moving on a free transfer from
Malaga.
He played under new City boss Pellegrini at
Malaga and River Plate, helping the former to the
quarter-finals of last season's Champions League.
His injury means he will miss Premier League
matches against Stoke City, Manchester United,
Aston Villa and Everton, plus Champions League
ties against Viktoria Plzen and Bayern Munich.
Matija Nastasic, the 20-year-old Serb, and
England international Joleon Lescott are the only
recognised central defenders available.
