In a post on Instagram this week, Neymar vowed to "come back stronger" after his injury.
"Neymar Jr was successfully operated on late this morning at the Aspetar Hospital in Doha...," PSG said in a statement.
The French champions did not provide a timeline for Neymar's return, saying "the player will now follow a protocol of rest and treatment."
Earlier this week, PSG said the injury will keep the Brazil international out for the rest of the season.
The Brazilian has twice spent lengthy spells on the sidelines after sustaining metatarsal fractures before PSG's last-16 tie against Real Madrid in 2019 and against Manchester United the following year, with the French side being knocked out of the Champions League on both occasions.
He did not feature in PSG's 2-0 defeat to Bayern Munich on Wednesday, which eliminated them from the Champions League.
PSG are top of the league with an eight-point lead over second-placed Olympique de Marseille. They next travel to 15th-placed Brest on Saturday.