The Dutch international, who returned to Hamburg this season after spells at Real Madrid and Tottenham Hotspur, was taken off clutching his thigh in the 33rd minute of the loss.
"I instantly had the feeling that it was a torn muscle," he told his club's website. "The injury hurts more than the defeat at the moment."
Team doctors said they also suspected a muscle tear and that more tests would be conducted.
Van der Vaart's form has lifted Hamburg up to ninth place this season as they eye a Europa League spot.