The Spanish striker had revealed the injury by posting a picture of his protective boot on social media on Monday, having been hurt in last Friday's 2-1 friendly victory over Hearts in Edinburgh.
Speaking at a press conference ahead of the club's match against Sporting Kansas City - the first of their pre-season tour of the United States - Pellegrini said Negredo had undergone surgery on his fifth metatarsal in his right foot.
"Alvaro had surgery today on his broken foot and he will probably be out for two or three months," he said.
"It is a blow for us because Alvaro is a very important member of our squad so obviously we will miss him."
The 28-year-old Negredo 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 after a shoulder injury 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.
Villa and option for City?
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.
However, Pellegrini hinted the club have not yet finished in the transfer market, with a move for Porto defender Eliaquim Mangala still expected, while several fringe players could leave.
"I don't think the squad is complete yet but we have six weeks before the transfer window closes," Pellegrini said.
"Perhaps there is the option to bring one or more players in or maybe one or two will leave our squad but there is time for us to consider what is best for our team."
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- Sporting Kansas City