The Dutchman, who has scored six goals in 12 league games this season, underwent medical checks following his injury during Netherlands' goalless draw against Colombia on Tuesday.
"He suffered a severe ligament injury in his ankle," Hamburg said in a statement, adding Van der Vaart had torn two ligaments. "It is not yet clear how long he will be out of action."
Netherlands have qualified for next year's World Cup in Brazil.
This is bitter news for the northern German club who are battling to stay clear of the bottom spots following two straight defeats that have left them in 14th place on 12 points, just four above the relegation playoff spot.
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