The Hamburg skipper was hurt in a heavy tackle during his country's goalless draw with Colombia in Amsterdam.
However, Van Gaal has revealed Van der Vaart has avoided significant damage.
"Thankfully he hasn't broken or ruptured anything," said the 62-year-old.
"I don't think he'll be able to play at the weekend, though (in Hamburg's Bundesliga meeting with Hannover)."
A statement from Hamburg confirmed the club were awaiting the results of an assessment, to be carried out on Wednesday afternoon, before putting a timescale on the player's absence.
Van der Vaart has started all 12 of Hamburg's league matches so far this season, scoring six goals.
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