Negredo confirmed the injury in a post on his Instagram page.
The injury came during City's victory over Hearts, a second-division Scottish club, in a friendly on Friday.
Negredo premiered for City in August 2013 and scored nine goals in the Premier League last season. He also scored five goals in UEFA Champions League play.
Despite scoring three goals in qualifying, he was left off Spain's roster for this year's World Cup.
Negredo will miss City's upcoming tour of the United States, which begins with a friendly against Sporting Kansas City on Wednesday.
- Dan Gartland