Dunga's side are to face Mexico on June 7 and Honduras three days later. Both games will take place on home soil but the venues are still to be decided.
Brazil launch their Copa America campaign, the first competitive matches since they were crushed 7-1 by Germany in last year's World Cup semi-finals, against Peru on June 14.
Colombia and Venezuela are the other two teams in Group C.
Later this month Brazil play friendlies against France in Paris and Chile in London.