Menezes replaced Dunga after the 2010 World Cup with a brief to lead the national team into their home finals four years later.
But failure at the 2011 Copa America and defeat in the final of this year's Olympic football tournament brought criticism back home.
And Menezes leaves with a record of 20 wins, six draws and five defeats from his time in charge.
Andres Sanchez, the Brazilian FA's National Teams Director, said a new manager would be appointed in January.
He added: "I don't think it was for negative results, if that was the case he could have been fired last year. It was that the president wants to change the way things are done."
Among those mentioned as favourites to take over are Luiz Felipe Scolari, who guided Brazil to their last World Cup triumph in 2002, and Tite, who took Corinthians to the Copa Libertadores title earlier this year.