The 30-year-old had to be helped off just before half-time in the Netherlands' goalless draw with Colombia in Amsterdam on Tuesday and an MRI scan in Hamburg confirmed a severe ligament injury in his right ankle.
The club have said there is no fixed date on how long he will be out for, but it is assumed at least the next four weeks and ex-Real Madrid star Van der Vaart could have played his last football of 2013.
"The loss really hurts, because he had played really well in the last last few weeks and had been an important part of the team," Hamburg's director of sport Oliver Kreuzer said.
"It all depends now on healing process, hope springs eternal."
With six goals in 12 Bundesliga games this season, the injury is a significant blow to Hamburg's attack with only Germany U-21 striker Pierre-Michel Lasogga, who has hit the net eight times in eight league games this season, having scored more goals for the Hanseatic side.
"I will do all I can to be back on the pitch as soon as possible," Van der Vaart said.
Hamburg, 14th in the league, have climbed out of the relegation places under ex-Dutch coach Bert van Marwijk, who replaced Thorsten Fink in September after a poor start to the season.