The former Barcelona player limped off the field 12 minutes into a friendly against Nigeria, held in Singapore on 13 October.
"Another assessment will be made in eight days, but initial estimates put his return to competition at four weeks, depending on how the injury progresses," PSG said in a statement on Monday.
Therefore, Neymar could miss PSG's upcoming UEFA Champions League clashes, both against Club Brugge on October 22 in Belgium and two weeks later in Paris.
Neymar had already missed the first couple of Champions League games against Real Madrid and Galatasaray as he served a sanction imposed for insulting referees last season.
Injuries have deprived PSG of the most costly player in history at several crucial moments.
Over the final stretch of the two seasons he has spent at PSG, Neymar suffered from a right foot problem that prevented him from helping the team advance at the continental club tournament.
He was at the center of the focus during the summer transfer window as he expressed his desire to leave the French club, but PSG's high financial demands blocked his departure.