The "top managers" of Herrira were detained in simultaneous raids carried out in the Basque cities of Hernani, Bilbao and Vitoria as well as in Pamplona in the Navarre region, which has a significant Basque-speaking population, it said in a statement.
Police also closed down 38 websites run by Herrira as well as dozens of Facebook and Twitter accounts, and froze the group's bank accounts.
Spanish authorities argue that Herrira, founded in February 2012, has replaced two other groups that provided aid to Eta prisoners, Askatasuna and Gestoras pro Amnistia, which were banned in Spain due to their close links to the armed separatist group.
The interior ministry said Herrira had taken over the task of "organizing and supporting demonstrations that praised and exalted Eta prisoners and their ideals", a role once played by Askatasuna and Gestoras pro Amnistia.
Eta is blamed for the deaths of 829 people in a four-decade campaign of shootings and bombings for an independent homeland in northern Spain and southern France.
In April a suspected top commander of Eta got a life sentence in France for the 2007 murder of two Spanish police officers.
Many more of its leaders have been arrested over recent years.
In October 2011 it declared a "definitive end to armed activity" but it has not formally disarmed nor disbanded as the governments of Spain and France demand.