Neymar was ruled out of the tournament with a ligament rupture in his right ankle, sustained during a 2-0 friendly win over Qatar.
The 27-year-old left the ground in tears as he was carried down the tunnel in the first half before the Brazilian Football Confederation (CBF) confirmed the PSG forward's absence from the Copa America, which starts on 15 June (AEST).
PSG reassessed Neymar and the Ligue 1 medical team reported that he will not require surgery, according to the club's doctors.
"Paris Saint-Germain's first team doctor, Dr Laurent Aumont, and the club's medical board member and leading figure in sport medicine Professor Gerard Saillant assessed the injury picked up by Neymar Jr in Brazil's preparation match for the Copa America last [Thursday AEST]," PSG's statement read.
"The two doctors diagnosed a sprain of the lateral ligament of the right ankle without surgical indication, to be treated with conservative treatment.
"The Paris Saint-Germain striker is expected to return on the field in four weeks' time."
Neymar has been replaced by Willian in Brazil's squad for the upcoming Copa America, which the Selecao will host after a friendly against Honduras on Monday (AEST).
PSG's Neymar netted 15 Ligue 1 goals and 23 across all competitions for the French champion in 2018/2019.