On Tuesday, the 27-year-old limped off the Granja Comary training pitch in Teresopolis, around 100km north of here, after awkwardly striking the ball with his left foot, reports Xinhua news agency.
Television footage showed the Paris Saint-Germain forward clutching his left knee and grimacing while being assessed by medical staff.
The Globo newspaper reported that initial scans showed no serious damage to the knee, but Neymar was due to undergo further tests on Wednesday.
The incident came just 17 days before the start of the Copa America, to be played in Brazil for the first time since 1989. The hosts will begin their campaign against Bolivia before also facing Peru and Venezuela in the group stage.
The five-time World Cup champions will prepare for the tournament with friendlies against Qatar on June 5 and Honduras four days later.
On Monday, the Brazilian Football Confederation announced that veteran full-back Daniel Alves has replaced Neymar as Brazil's captain following a series of controversies surrounding the former Barcelona and Santos star.
Earlier this month Neymar was banned for three matches by the French Football Federation for punching a fan after the French Cup final. In April, he was suspended for three UEFA Champions League games for insulting officials following Paris Saint-Germain's elimination from the tournament.
( With inputs from IANS )