The video showed Krause's passport and was posted on Saturday. It showed a masked man reading: "We give the German government 10 days from the date of this statement to announce and start the withdrawal of their troops from Afghanistan, otherwise ... they will not even see the bodies of these two agents."
He did not give the date of the statement.
The speaker said Germany was "annihilating" fellow Muslims in Afghanistan and "smiling at us in Iraq. Do not the tyrants know that we are one nation with one religion?"
Germany opposed the 2003 US-led invasion of Iraq.
Krause, 61, was sitting next to a younger man. In the video she urged Angela Merkel, the German chancellor, to meet the demands of her abductors to save her life and that of her son. Both hostages were weeping as she made her plea.
It was not clear if the man was also German, but Krause said that he had recently married and that his wife might be pregnant.
Her German-language statement was translated into Arabic on the video.