Neymar came off after 25 minutes in Istanbul on Wednesday. PSG went on to win 2-0.
“The Brazilian, who had tried to play on before asking to be substituted, underwent an MRI scan that revealed a tear to the adductor,” the RMC Sport website said.
PSG’s next three games are a Ligue 1 match in Nantes on Saturday, followed by home games against RB Leipzig in the Champions League on Wednesday and Rennes in Ligue 1 on November 7.
That game is followed by an international break when Brazil are due to face Venezuela and Uruguay in World Cup qualifying.
“No indication has yet been given of his participation in the Brazilian national team’s gathering,” RMC Sport said.
PSG coach Thomas Tuchel was already dealing with a full infirmary, with Marco Verratti, Mauro Icardi, Leandro Paredes, Julian Draxler and Juan Bernat all hurt.
After missing the start of the season due to Covid-19 and then two more games following his red card against Marseille, Neymar has scored twice and had four assists this season.