The raids came as the government banned the group, which it accused of trying to recruit fighters for so-called Islamic State (IS).
An Interior Ministry spokeswoman said there was no indication DWR (True Religion) was planning attacks itself.
She said the group had breached the constitution and incited hatred.
There was no immediate statement from the group.
Some of those who have gone to fight for IS in the Middle East had contact with the organisation before they left.
Officials estimate that almost 900 people in total have so far left Germany to join IS in Syria or Iraq.
"The message to the radical Islamist scene is clear: we do not tolerate fanatics who try to radicalise young people and send them to jihad," said Peter Beuth, interior minister for Hesse state, where some of the raids took place.
"By banning this organisation, a major source of radicalisation has been eradicated nationwide. Those who spread hate messages can`t hide behind freedom of religion."
German raids: Police target DWR Islamist group
15 November 2016
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German police have carried out nationwide dawn raids on more than 200 mosques, apartments and offices associated with an Islamist group.
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