The midfielder, who played a pivotal role in Les Bleus's winning campaign in 2018, suffered a setback in the final stages of his recovery last week and has now been ruled out for four months after the surgery.
Kante's early season has been marred by the hamstring problem that has now ruled him out of selection for the World Cup in Qatar.
He has only featured in two Premier League games and played a total of 175 minutes this season.
"The midfielder visited a specialist with the club's medical department to explore the options for his rehabilitation approach and it was mutually agreed for N'Golo to have surgery to repair the damage," Chelsea said in a statement.
Kante has been a vital player for Chelsea since his move from Leicester City in 2016 and equally important for France, having earned 53 caps.
Coach Didier Deschamps had warned that he would not pick any player who would not be fit for the start of the tournament.
He now faces some tricky choices before naming his squad on November 9th as another key midfielder, Paul Pogba (29), is a doubt after the Juventus player underwent knee surgery last month.
France were drawn in Group D with Australia, Denmark and Tunisia.
