The 21-year-old was arrested shortly before 11am and was being detained at Dungarvan Garda station in Co Waterford.
His body was discovered in a cell before noon on Tuesday.
The Garda Ombudsman - the force's official watchdog - has been called in to investigate the circumstances surrounding the death.
A spokesman said a post mortem will be carried out tomorrow at Waterford Regional Hospital.
It is understood the man, who is from the Dungarvan area, was under arrest for a minor public order offence when he died.
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