Oscar has not been included in a 23-man Brazil squad featuring four Premier League players, including his team-mates Filipe Luis and Willian.
And Dunga said the player, who did not feature on Sunday as Chelsea beat Crystal Palace to win the Premier League, has been ruled out with an injury suffered during a training session.
“We spoke with Jose Mourinho and the doctor at Chelsea,” he said. “Oscar’s recuperation will take time and he won’t be at his best during the Copa America.
“After the Copa America we have the World Cup qualifiers, and we thought it best for him to be ready for the qualifiers.”
Porto’s Casemiro has been called up to replace Oscar, while Philippe Coutinho of Liverpool is named along with Manchester City’s Fernandinho.
Squad: Jefferson, Diego Alves, Marcelo Grohe, David Luiz, Marquinhos, Thiago Silva, Miranda, Fabinho, Marcelo,
Filipe Luís, Danilo, Luiz Gustavo, Fernandinho, Elias, Souza, Everton Ribeiro, Douglas Costa, Willian, Philippe Coutinho, Neymar, Diego Tardelli, Robinho, Firmino.