Van der Vaart picked up the knock during Tuesday's training session at Netherlands' camp in Portugal and he has now been ruled out of the finals as a result.
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The 31-year-old was widely expected to make Holland's final 23-man squad for the tournament in Brazil, but his physical problems will now prevent him from making it to the third World Cup of his career after previously featuring in 2006 and 2010.
Van der Vaart was the most experienced player in Oranje's squad, having made 109 appearances for the national side since making his debut under Van Gaal back in 2001.
The Hamburg star's withdrawals is yet another blow for the 2010 World Cup runner up after the previously confirmed absence of Kevin Strootman and Gregory van der Wiel due to injury, too.
The midfielder will likely be replaced by either PSV skipper Georginio Wijnaldum or Feyenoord youngster Tonny Vilhena.
Netherlands meets Spain, Australia and Chile in Group B this summer.