The 26-year-old Belgian suffered the problem in his side's 3-1 friendly defeat against Sunderland in Hong Kong on Wednesday, and is now doubtful for Tottenham's opener with Crystal Palace on August 18.
Vertonghen turned awkwardly before being taken off on a stretcher, although manager Andre Villas-Boas is still hopeful he could recover in time.
"Jan has had damage to his ligaments and he's going to be most likely out of training for two to three weeks," the Portuguese said.
"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."
The pre-season Asia Trophy clash in Hong Kong was reduced to 40 minutes per half because of torrential rain, with the condition of the pitch quickly deteriorating.
Villas-Boas admitted he had been "concerned" by the surface, saying afterwards: "The pitch is always like that for this tournament. You can’t change the conditions, they are extremely poor."
