The arrest was made as gardai 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.”
It is understood the person targeted by the alleged threat is a Westminster MP.
The Irish Times has reported that the person is a female Labour politician.
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, as he held a constituency surgery in Leigh-on-Sea in Essex on October 15.
Ali Harbi Ali, 25, has been remanded in custody charged with murdering Sir David.