Capped 109 times for his country, the 31-year-old Hamburg player suffered the injury at a training camp for the tournament on Tuesday with team officials saying he was not expected to recover in time to participate in the finals.
Van der Vaart sat out training on Monday because of a fever before conducting an individual session on Tuesday while the rest of his team mates were preparing to leave the Algarve at the end of the camp.
It was during this session that he was injured but the extent of the tear was only confirmed after medical examination in Amsterdam yesterday. The KNVB then confirmed that his hopes of playing in a third World Cup were over.
The former Ajax, Real Madrid and Tottenham Hotspur midfielder competed at the last two finals and was expected to a play a major role for the team in Brazil. His injury means the Dutch have lost two key midfielders in the run-up to the tournament with Roma's Kevin Strootman ruled out in March through a serious knee injury.
Van der Vaart had struggled with the calf injury throughout the recently concluded Bundesliga season in which his club narrowly avoided relegation.
The Dutch are expected to name their final 23-man squad for Brazil on Saturday. They meet Spain in their opening Group B fixture on June 13, followed by Australia on June 18 and Chile on June 23.