The 30-year-old sustained the injury on international duty with the Netherlands during a goalless draw with Colombia on Tuesday.
Medical staff at Hamburg initially predicted Van der Vaart would be "missing for some time", but the player took to Twitter on Wednesday to reveal his expected return date.
"Maybe you've heard it already, it will take 3 to 4 weeks to recover from my ankle injury," he wrote.
"Will work as hard as I can to be back asap!"
The Dutchman has scored six goals in 12 Bundesliga matches this season and is set to miss a busy period for his club.
Hamburg face six fixtures over the next four weeks, but Van der Vaart will be hoping to make an early return in time for the trip to Bayern Munich on December 14.
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