The 32-year-old replaces Real Madrid-bound right-back Danilo, who picked up an injury in Sunday’s 2-0 victory over Mexico.
Alves, who signed a two-year contract extension at Barca on Tuesday, has not featured for his country since Brazil’s World Cup campaign ended in a 7-1 semi-final defeat to Germany last year.
He was dropped by Luiz Felipe Scolari at the quarter-final stage in that competition and has not made a single Brazil squad since the arrival of Dunga as coach.
A statement on the Brazilian Football Federation’s (CBF) website confirmed Danilo has failed to recover from an injury to his right ankle and will shortly leave the camp to continue his rehabilitation in Madrid.
The injury is not expected to prove serious enough to delay the start to his career at the Bernabeu.
Danilo is the fourth member of Brazil’s Copa America squad to withdraw through injury, with Dunga having already lost Luiz Gustavo, Diego Alves and Marcelo from his original list of 23.