Van der Vaart sidelined for six weeks
Van der Vaart, 28, missed the Netherlands' record 11-0 victory over San Marino in their Euro 2012 Group E qualifier on Friday and will miss their next qualifier against Finland on Tuesday.
He is also unlikely to be fit in time for the group leaders' final two qualifiers against Moldova and Sweden in October.
Spurs, who have made a poor start to the new season with two defeats in their opening two matches, said on their website, than an MRI scan showed the tear in Van der Vaart's left hamstring.
He will miss at least the next four Premier League matches for Spurs as well as their opening Europa League fixtures against PAOK Salonica and Shamrock Rovers.
Van der Vaart joined Spurs from Real Madrid on the last day of the transfer window in August last year and was their top scorer in the league last season with 13 goals in 28 appearances.