The 36-year-old, identified only as Wojciech G, is accused of molesting boys while serving as a parish priest on the Caribbean island.
He denies the accusations.
Last year Polish archbishop Jozef Wesolowski was recalled to Rome amid claims he sexually abused children in the Dominican Republic.
The 65-year-old archbishop, formerly the Vatican's representative to the island, is one of the highest ranking Catholic Church officials to be investigated for alleged abuse.
In the latest case, Wojciech G was arrested at his home near Krakow on Monday and is expected to be formally charged on Tuesday.
The BBC's Adam Easton in Warsaw says the Catholic Church in Poland has largely been spared the sex abuse scandals that have made headlines in Ireland or the US.
But this case - and similar accusations against Archbishop Wesolowski, who served as the Papal Nuncio in the Dominican Republic until last August - are starting to change that.
Earlier this month, a Polish man who was abused by a priest as a child announced he was suing the country's Roman Catholic Church - the first such civil case in the country.
The church leadership apologised to all child abuse victims last year, but insisted it would not pay damages for the crimes of individual clergymen.
Meanwhile, the UN has said the Vatican should "immediately remove" all clergy who were known or suspected child abusers.
In a report, the UN Committee on the Rights of the Child also denounced the Holy See for adopting policies which allowed priests to sexually abuse thousands of children.
Police in Poland have arrested a Catholic priest suspected of committing sex offences against children in the Dominican Republic.