The Spain international picked up the injury during City's 2-1 friendly win over Hearts on Friday evening.
Negredo, who has fractured his fifth metatarsal, has uploaded a picture to his Instagram account of his foot in a plastic cast.
Alongside the image, he posted the message: "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. I will be back stronger than ever."
Reports have suggested that Negredo will miss the first two months of the season.