Federal prosecutors said that the "Freital Group," named after a suburb of the eastern city of Dresden that has seen a string of anti-refugee protests and other incidents, was formed in July last year or earlier.
They said several apartments in the state of Saxony were searched alongside the arrests of the five German nationals four men and a woman aged between 18 and 39.
The group acquired more than 100 firecrackers of various types from the Czech Republic, prosecutors said in a statement.
Prosecutors are looking into whether they were behind any further attacks.
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The suspects were identified only as Justin S., Rico K., Maria K., Sebastian W. And Mike S. In line with German privacy rules.
As well as membership in a terrorist organization, they are also suspected of offenses including attempted murder, bodily harm and bringing about explosions.
Germany saw a surge in far-right attacks over the past year amid a huge influx of refugees and other migrants.