Vertonghen slipped on the rain-soaked pitch after coming on as a second half substitute against Sunderland and was unable to continue.
The Belgium international was taken to hospital for scans which have confirmed the extent of the damage to his ligaments.
The 26-year-old has been ruled out for up to three weeks - meaning he is facing a battle to be fit in time for Spurs' opening Premier League fixture against Crystal Palace on August 18.
Tottenham boss Andre Villas Boas said: "Jan has had damage to his ligaments and he's going to be most likely out of training for two to three weeks.
"So just about on the deadline for the first game of the season.
"Hopefully we can see a bigger recovery time with him - hopefully we can have him back sooner."