The Spain international, who played the first half of City's friendly victory over Hearts on Friday, has broken the fifth metarsal in his right foot.
"I want to let you know that its going to be hard for the next few months, I fractured my 5th metatarsal and will be out a few months," Negredo wrote on his Instagram account with an accompanying picture of him wearing a protective boot.
"I will be back stronger than ever. I will return with avengeance."
Negredo appeared to sustain the injury shortly after setting up City's opening goal against Hearts by Scott Sinclair with a brilliant through-ball, limping off just before the break.
The 28-year-old joined City from Sevilla a year ago in a £16million-plus deal and quickly became a fans' favourite after making an immediate impact.
He scored an impressive 23 goals in his first 33 games in all competitions, including City's first Champions League hat-trick in the 5-2 win over CSKA Moscow.
However, from mid-January onwards he began to struggle and in 16 subsequent matches up to the end of the season he failed to score, which put additional pressure on City's other strikers and midfielder Yaya Toure to come up with the goals which secured them a second Premier League title in three years.
Earlier in the summer City manager Manuel Pellegrini was reported to be willing to listen to offers for the striker and Negredo was linked with a move back to Spain to rejoin former club Real Madrid for a second time, but his injury setback looks to have ended that prospect.