The club updated Kane's condition on Thursday after initially diagnosing the injury last week.
Kane ruptured a tendon in his left hamstring while taking a shot against Southampton on New Year's Day.
"The decision to undergo surgery is not expected to impact the time frame that the England captain will be sidelined, with the expectation that he will return to training in April," Tottenham said in their statement.
Kane is now set to miss at least 13 matches across all competitions, including both legs of Tottenham's last-16 clash with RB Leipzig. The Premier League season will end on May 17.