Teh group, called The Voice of the Caliphate, issued its warning in a video statement posted on the Internet.
A German Foreign Ministry spokesman told AFP that "the video is currently being evaluated by government experts."
The new clip follows an Internet video in which Iraqi militants holding a German woman and her son captive threatened to kill them unless Germany withdraws its forces from Afghanistan within 10 days.
Germany has some 2,800 troops in northern Afghanistan as part of NATO's International Security Assistance Force (ISAF).
Berlin has resisted NATO pressure to allow German troops to be deployed to the more violent regions in southern Afghanistan.
The group's video also threatens "mujahedin" targeting of Austria, which reportedly has five military officers stationed in Afghanistan.
(AFP, AP, dpa)