The 30-year-old suffered the injury in the 4-4 draw at Chelsea on Sunday.
Brazil's national team doctor Rodrigo Lasmar said: "He suffered trauma to his foot in the final minutes and was able to continue the match but the pain became intense. The foot became swollen, making it difficult to walk."
Meanwhile, defender Nathan Ake - who missed the game at Stamford Bridge - has pulled out of the Netherlands squad. However, there are not yet details of what his injury is.
Manchester City host second-placed Liverpool at 12:30 GMT on 25 November in the first game after the international break.