The centre-back played the full 90 minutes of Spurs' defeat by Newcastle United on the opening day of the season but was then absent for the draw against West Brom.
France international Kaboul, who missed Euro 2012 with a knee injury, has now confirmed he has had an operation and will require up to four months of rehabilitation.
The news will come as a setback for Tottenham boss Andre Villas-Boas but he does have cover after summer signing Jan Vertonghen impressed on his debut against West Brom.
Kaboul said on Twitter: "Morning all, surgery done with success. Now looking forward for my rehab. I thank you all for your great support as usual!#comingbackstronger.
"Sorry I forgot to mention how long...Should be 4 months."
It remains to be seen whether Kaboul's injury alters Tottenham's decision to put Michael Dawson, who was wanted by Queens Park Rangers, up for sale.
Villas-Boas also has 20-year-old Steven Caulker as another potential central defensive option ahead of Saturday's Premier League game against Norwich City at White Hart Lane.
