Kane suffered the injury during the 1-0 Premier League defeat at Southampton on New Year's Day and specialists advised an operation was needed.
A Tottenham club statement read: "Following ongoing assessment by our medical staff over the past week, we can confirm that Harry Kane will undergo surgery to repair a ruptured tendon in his left hamstring.
"The striker suffered the injury during our Premier League fixture against Southampton last week and specialists have advised surgery after further review of the injury.
"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."
The news presented another headache for Spurs boss Jose Mourinho, who has also seen midfielder Moussa Sissoko sidelined until April after undergoing knee surgery.
Spurs also have first-choice goalkeeper Hugo Lloris recovering from injury, along with summer signing Tanguy Ndombele as well as full-back pairing Danny Rose and Ben Davies.
Kane will now also miss England's friendlies against Italy and Denmark at the end of March.
However, if all goes well in his rehabilitation, Kane should be back in good time to lead the Three Lions into Euro 2020.