The midfielder, 24, has not played since August 28 after suffering a recurrence of the ankle injury which dogged him throughout last season in the 5-1 defeat against Manchester City.
Last week Spurs boss Harry Redknapp announced that Huddlestone would require an operation on the injury - his second in the space of 11 months - and the club confirmed the operation took place on Friday.
A club statement read: "Tom Huddlestone has today (Friday) undergone a surgical procedure to his right ankle.
"The midfielder will be further assessed by the specialist in six weeks' time, after which a time frame for a return to training will be determined."
Huddlestone has established himself as a key figure in the Spurs set-up in recent years following his move to White Hart Lane from Derby in July 2005.
He made more starts than any other outfield player in all competitions in the 2009-10 season, but was sidelined for five months last term due to the problem with his ankle.
Despite being a key member of the Spurs line-up for the last two years, his absence has not been too greatly felt at White Hart Lane this year thanks to the performances of new signing Scott Parker and Sandro, and the emergence of young midfielder Jake Livermore.