The 27-year-old Schalke 04 player injured himself during Germany's 3-0 friendly win over Hungary in Budapest on Saturday.
His injury is the latest blow for Germany who are already without captain and Chelsea midfielder Michael Ballack and midfielder Christian Traesch, both out with ankle injuries.
"Heiko would have played a key role in our team. He would have been important for us because of his polyvalence," said Germany coach Joachim Loew. He showed remarkable form in training."
Germany face Australia, Serbia and CAF Africa Cup of Nations finalists Ghana in Group D at the FIFA World Cup, which runs from 11 June - 11 July in South Africa.