The Netherlands international was taken off after 52 minutes in the 4-2 defeat to Eintracht Braunschweig on Saturday.
In a statement on their official website, Hamburg confirmed that the 31-year-old suffered "torn ligaments in his right ankle" during the fixture.
He will likely miss Bundesliga fixtures with Borussia Dortmund, Werder Bremen and Eintracht Frankfurt with managerless Hamburg currently second bottom in the German top flight.
The club dispensed with the services of Bert van Marwijk on Saturday after slumping to a seventh straight league defeat at the Eintracht-Stadion.
Former Schalke and Hannover coach Mirko Slomka has been touted as the man likely to replace Van Marwijk.
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