The Brazilians drew 0-0 with Ecuador and beat Haiti 7-1 but were beaten 1-0 by Peru to exit the competition at the group stages for the first time since 1987.
Dunga, who was in his second spell as Brazil coach, was fired after a meeting at the CBF in Rio de Janeiro.
"The Brazilian Football Confederation decided this Tuesday to dissolve the technical commission of the Brazilian national team," the CBF said in a short statement.
"National teams coordinator Gilmar Rinaldi, coach Dunga and their entire team will leave their posts.
"The CBF has began the process of choosing a new technical commission for the Brazilian team."
The overwhelming favourite to become Brazil's new coach is Corinthians 55-year-old manager Tite.
The new man will also be charged with leading the under-23 squad in August's Olympic Games in Rio de Janeiro, the only major tournament Brazil have never won.
Tite led Sao Paulo's biggest club to Brazil's Serie A title in 2011 and 2015 as well as the Copa Libertadores and World Club Cup for the first time in 2012.
Dunga had never coached until he was first hired as Brazil boss in 2006. He led them to the Copa America in Venezuela in his first major tournament the following year.
He was fired in 2010, immediately after Brazil were eliminated by the Netherlands at the quarter-final stage of that year's World Cup.
After coaching his boyhood club, Internacional, for a year in 2013, Dunga was a surprise choice to replace Luiz Felipe Scolari after Brazil's humiliating 7-1 loss to Germany in the 2014 World Cup.
Dunga, who was captain of Brazil's 1994 World Cup winning side, was given the task of revamping the national set-up but his defensive style of play and curt manner won him few fans.
Led by Barcelona striker Neymar, Brazil performed well in friendlies, but were knocked out of the 2015 Copa America at the quarter-final stage by Paraguay and, without several first-team players, they were poor again at this year's tournament in the United States.One of the main priorities for the new boss will be ensuring Brazil qualify for the 2018 World Cup in Russia. After a poor start, Brazil sit in sixth place in the South American qualifying group.
The top four teams qualify automatically for the tournament and the fifth-placed side enter an inter-continental playoff.
(Writing by Andrew Downie; Editing by Toby Davis)
