The Paris Saint-Germain forward has had another injury-hit campaign but has returned to fitness in time for this year's tournament.
Neymar appeared to be affected by the burden of expectation on his shoulders when playing for Brazil at the World Cup last year.
PSG manager Thomas Tuchel has ruled out making Neymar captain of his club, preferring to keep faith with compatriots Thiago Silva and Marquinhos.
Brazil starts its Copa America campaign with group games against Bolivia, Venezuela and Peru, and Edmilson has told Selecao coach Tite to look elsewhere for his captain.
"It's a squad list where there are people with experience and who were already captains," the former Barcelona and Brazil defender said. "In my opinion, this is not the ideal time to deliver the armband to Neymar, but the final decision is with Tite.
"The list has once again been the subject of debate, the diversity of players is good and we have several alternatives in each position.
"It is clear that Tite feels the pressure of having to win this Copa America at home, these have been chosen by the coach to get the title."
Tite left out Real Madrid duo Marcelo and Vinicius Junior for his Copa America squad, with Porto full-back Alex Telles another notable absentee.
Brazil faces Qatar and Honduras in pre-tournament friendlies before getting the tournament underway on 14 June.