Federation director Andres Sanchez said the decision to fire the coach came after a meeting in Sao Paulo on Friday.
He said federation president Jose Maria Marin made the change because he "wants new methods and new planning" ahead of the 2014 World Cup that Brazil will host.
World Cup-winning coach Luiz Felipe Scolari is one of the names touted to replace Menezes, but Sanchez said he doesn't think negotiations for a new coach are under way.
Sanchez, the federation director in charge of the national team, made it clear that he didn't agree with the decision to fire Menezes. But he said the president was being "brave" and called it a "bold" move to make the change.