The Brazilian Football Confederation confirmed the decision following a meeting of their hierarchy.
Squad director Andres Sanchez revealed a new boss would be announced at the start of January and there were at least seven candidates in contention.
Sanchez did not give any names, but local reports named former Barcelona boss Pep Guardiola along with Luiz Felipe Scolari and experienced coach Muricy Ramalho as the leading contenders.
Confederation president Jose Maria Marin and vice-resident Marco Polo del Nero were also present at Friday's meeting, where the decision to dispense with Menezes was made.
Sanchez appeared to question the move, saying: "I respect and understand the arguments of the directors, but I think this isn't the correct moment."
"But I understand the criteria. It's the president's decision and he wants different methods for the next year.
"He's a brave man, he's watching the future, so we have to respect him.
"Mano did a good job, even though he had tough times. He did not leave because of bad results. If the results were the key, he would have left the national team at the start of the year, not now.
"The president wants to change the methods of the national team from January."
Menezes' dismissal comes just two days after Brazil won the Superclasico de las Americas against Argentina on penalties.
Brazil lost the second leg 2-1 in Buenos Aires, but triumphed on spot-kicks in the tie which featured only players who play in the two countries' domestic leagues.
Menezes lasted little more than two years in the job, having been appointed after the 2010 World Cup as the replacement for Dunga.
He failed to deliver an expected Olympic gold medal at London 2012, though, as a team which featured the likes of Neymar and Oscar lost to Mexico in the final.
Menezes' first major tournament in charge of the five-times world champions ended in disappointment as Brazil were beaten in the quarter-finals of the Copa America last year.
They lost on penalties to Paraguay, missing all four of their spot-kicks.
The team's form improved this year, but it was not enough to keep him in his job and Brazil are now searching for their fourth coach since they last won the World Cup a decade ago.
Menezes said on Twitter: "As it has been announced, I'm not the national coach anymore.
"My thanks to all the people who worked with me on this project, specially the players that were called up during this period and all those who believed in our work."
Former Brazil striker Romario and former defender Juliano Belletti both backed Scolari, who led the country to their last World Cup triumph, to take the reins.
Romario said: "The best man is Felipe, no doubt about that. And I also believe that Andres Sanchez can't continue as general manager, Rai is the correct man for the job."
Belletti added on Twitter: "The World Cup is only seven games, kill or be killed. Felipe is very good on that. He motivates you, and demands things from you."