The 30-year-old suffered the injury during his country's goalless friendly with the South American outfit in Amsterdam, and the extent of the problem has now been determined by medical tests.
"Rafael van der Vaart has suffered severe ligament injury in the right ankle," a statement on Hamburg's official website read. "One of the interior ligaments in the foot is torn ligaments and (he has) a torn outer ligament.
"Much has been speculated about the severity of his injury, now it is clear that the ligaments were severely affected in his right foot and he will be missing for some time."
Van der Vaart has started all 12 Bundesliga matches for Hamburg this season - scoring six goals - and sporting director Oliver Kreuzer admitted the injury comes as a blow to the club.
"The loss hurts already, because he has played very strong, especially in recent weeks, and otherwise is an important part of the team," he said.
"(How long he is out) depends on the healing process ... Rafa has good healing flesh."
