The 31-year-old defender was injured in the Premier League win at Huddersfield last month.
“The Belgium international defender will now continue his recovery with a view to returning to full training by December,” Spurs said in a brief statement on their website.
Vertonghen is set to miss the Champions League double header with PSV Eindhoven, which could see Spurs eliminated from the competition after earlier losses to Inter Milan and Barcelona.
He sustained the injury in a collision with Huddersfield striker Laurent Depoitre early in the game on September 29 but continued until half-time, thinking it was a dead leg.
Spurs, fifth in the Premier League, have a host of injury concerns.
Danny Rose withdrew from England duty this week with a groin problem while Christian Eriksen, Mousa Dembele, Dele Alli, and Serge Aurier have also missed recent matches.
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