Raids were continuing Wednesday morning targeting the group, based on the island of Mallorca and led by an Islamist imam, who was arrested in Britain, the ministry said in a statement.
The imam, 44, was the target of a European arrest warrant and seized by the West Midlands Counter Terrorism Unit on behalf of the Spanish authorities.
"The investigation focuses on terrorism material created for use online," the West Midlands police said, adding that prosecutors would seek his extradition to Spain later Wednesday.
The investigation began in 2015 after authorities discovered videos posted to the internet describing a young Muslim living in Spain and his radicalisation, and his eventual departure for Syria.
The imam, "whose public discourse was well known to European police and intelligence services, focused in private on the recruitment of fighters and collecting funds for Syria," the Spanish interior ministry said.
The group organised "weekly underground meetings... of youths with similar ideologies... to convince them to travel to conflict zones," the ministry said.
"The group's engagement and total allegiance to Daesh (IS) directives, the defence of terrorist actions carried out by lone operatives in Europe, and its readiness to carry out violent jihad, justified this operation."
Four arrests were also made in Palma, the capital of Mallorca, and one in Germany, and searches were still underway in Germany and Britain.
The intelligence and police services of Spain, Britain and Germany, along with European agencies, took part in the raids coordinated by the Spanish state prosecutor, which oversees terrorism cases.