Van der Vaart, who returned to Hamburg this season, has helped lift the northern club off bottom spot in the Bundesliga and back into contention for a European place.
"Tests on Sunday morning showed that it was indeed a muscle tear. He is expected to be out for three weeks," the club said in a statement.
Hamburg will also miss Son Heung-min for Tuesday's home league game against third-placed Schalke 04 with the South Korean, who has already scored six goals this season, suffering a muscle strain against Dusseldorf on Friday.
Hamburg, the only Bundesliga club never to have played in the second division since the top flight was introduced in 1963, are in 10th place on 17 points with Schalke on 24.