PSG wrapped up the French top-flight title with five games to spare when they demolished nearest rivals Monaco 7-1 last month.
Verratti also does not have World Cup commitments to worry about after Italy failed to reach Russia 2018, although the 25-year-old will miss his club's attempts to complete a domestic treble in the Coupe de France final against third-tier minnows Les Herbiers next Tuesday.
"The operation went perfectly," read a brief statement on PSG's Twitter.
"The date was chosen to allow Marco Verratti to resume the 2018-19 season in the best conditions."
The 25-year-old played 38 matches for PSG this season, scoring two goals and adding seven assists.
PSG travel to Amiens in Ligue 1 on Friday and will also be without captain Thiago Silva and winger Julian Draxler due to muscular complaints.
Neymar is expected back in France by the time that match is played, though it remains doubtful that the Brazil international star will play again for the French champions this season.