The 41-year-old has been detained in the Cork suburb of Douglas in connection with death threats made against a female MP for the Labour Party.
The arrest was made as garda - the national police force in Ireland - executed a search warrant at a residential property.
A Garda spokesman said: “During the course of the search a number of electronic items were seized and one man, 41, was arrested on suspicion of making threats against a person from outside of this jurisdiction.”
The man has been detained under Section 4 of Ireland’s Criminal Justice Act. He is being held at Bridewell Garda Station in Cork.
The arrest follows the fatal stabbing of Conservative MP Sir David Amess on October 15.