"Iruretagoyena is considered by the maximum expert in the making of bombs within Eta," he said at a press conference in Madrid.
The operation comes less than a week after the group carried out its first attack after ending its ceasefire on 5 June.
The other suspects were identified as Ander Múgica Alaitz Aramendi, Alaitz Aramendi Jaunarena and Ohian Barandalla and investigations were ongoing, the minister said.
The Spanish government had attempted to hold peace talks with Eta last year but called them off after the explosion.
The group, whose name is a Basque-language acronym for Basque Homeland Freedom, has killed more than 800 people since 1968 in an armed campaign for independence for the Basque territories in northern Spain and southern France.