Vertonghen has not featured for Spurs since being substituted with the problem in the 45th minute of a 2-0 win over Huddersfield Town on 29 September.
He was omitted from Roberto Martinez's latest Belgium squad to remain with Tottenham, where he has been monitored closely by the club's medical staff.
A statement issued on the club's official website said: "Jan Vertonghen sustained a hamstring injury against Hudderfield Town on 29 September, which has been monitored closely over the past 12 days.
"Further investigation has shown a good initial response to rehabilitation. The Belgium international defender will now continue his recovery with a view to returning to full training by December."
Vertonghen's injury is a further blow to Mauricio Pochettino, who is currently without Christian Eriksen (abdominal), Dele Alli (hamstring), Mousa Dembele (thigh), Danny Rose (groin) and Serge Aurier (thigh) due to muscle problems.
England confirmed earlier on Thursday that Rose had returned to Tottenham for rehabilitation work after reporting for international duty with the injury.
Tottenham's first match after the October international break will be a feisty London derby against rivals West Ham at the London Stadium on 20 October.
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