The 74-year-old Spanish national was held in the northern city of Miranda de Ebro and a search of his home was “still underway” on Wednesday, said Spain’s interior ministry.
Police said the suspect was “very active” on social media.
Authorities “do not rule out the participation or influence of other people” in the case, the force added.
A worker at the Ukrainian embassy in Madrid suffered minor injuries while handling a letter in November.
An explosive device sent by regular post to Prime Minister Pedro Sanchez was destroyed by the bomb squad the same month.
Similar letters were sent to Spain’s defence ministry, a European Union satellite centre at the Torrejon de Ardoz air base near Madrid and an arms factory - which makes grenades sent to Ukraine - in north-east Spain.
An envelope intercepted at the American embassy’s security screening point in December was also detonated by authorities.