Neymar limped off in the 12th minute on Sunday as Brazil drew 1-1 against Nigeria in a friendly in Singapore.
PSG said that an MRI scan showed that their star player had suffered "a grade two lesion" in his left hamstring.
If he is out until November 11, Neymar will miss four French league matches, including a trip to Marseille on October 27, and home and away Champions League games against Bruges.
The world's most expensive player had been due to make his champions League return against Bruges next Tuesday after serving a two-match suspension.
This latest in a catalogue of injuries since joining PSG in 2017 came after a promising start to the season with four goals in five Ligue 1 matches.
Sanchez could need ankle surgery: Chile coach
Inter Milan attacker Alexis Sanchez could be out for three months with an injury suffered in a friendly international against Colombia, Chile coach Reinaldo Rueda said on Monday.
Sanchez went off with an ankle problem in the 88th minute of the goalless draw in Alicante on Saturday.
Chile play Guinea on Tuesday in another friendly, also in the Spanish resort, but Rueda said he was worried that the former Arsenal and Manchester United player might miss the start of South American World Cup qualifying in March.
"We have to see what diagnosis they make in the club, because it is decisive for us," the Chilean coach said. "If there is surgery we could lose him two to three months, if not, it could be a matter of weeks. That depends on the club. They own the player."
Sanchez has left the Chilean training camp and returned to Milan.
Inter have yet to provide official information about the severity of his injury.
"For us, Alexis is very important," Rueda said. "For Inter, he's just another player. If he gets injured, buy another one."
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