Neymar had said he wanted to be one of Brazil's three permitted over-age players at the Rio Games in his home country in August, while coach Dunga had also hoped to have the 24-year-old available for June's Copa America Centenario.
However, the 70-cap international - who was in the Brazil team that lost in the final of the 2012 London Games against Mexico - has been freed from taking part in the centenary tournament in the United States.
"Barcelona thanks the Brazilian Football Confederation, and its president Marco Polo del Nero, who have accepted the proposal made by the club in order for the player Neymar only has to play in the Olympic Games in Brazil 2016, which take place between August 3 and 21," the La Liga champions said in a statement after Neymar scored in Barca's 8-0 rout of Deportivo La Coruna on Wednesday.
"In this way, Neymar is freed from playing at the Copa America, which will be played in the United States between June 3 and 26.
"The club wants to thank all the parties involved."
Brazil and Neymar have been drawn alongside South Africa, Denmark and Iraq in Group A of the men's football tournament.
The host nation kick-off their campaign against South Africa at Estadio Nacional Mane Garrincha in Brasilia on August 4.