Negredo posted a photo on social media of his right foot in a protective boot and said the injury was to his fifth metatarsal.
An accompanying message said: "I want to let you know that its going to be hard for the next few months. I will be back stronger than ever. I will return with a vengeance."
The Spain international, who played 45 minutes as Premier League champions City beat Hearts in a pre-season friendly on Saturday, did not say how the fracture happened.Negredo scored 23 goals in his first season at City, but the last of them came in January and he was linked with a return to Spain earlier this summer.
Speaking this week on the club's television channel, the 28-year-old denied the rumours of a departure, saying: "I don’t want to leave City. I’m very happy and very settled here.
"I had a difficult end to the season and that’s why there has been a lot of talking but I’ve been very happy here from the first day I arrived."
Negredo appeared to sustain the injury shortly after setting up City's opening goal by Scott Sinclair in the 2-1 victory with a brilliant through-ball, limping off just before the break at Tynecastle.
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.
@altamont...maybe they should ban him for a few months? Sad news for City though, let's hope Aguero and Jovetic manage to stay fit for more than a couple of consecutive games.- bernsteinforpm