Retired telecoms engineer Alec Warburton, 59, has not been seen since 31 July.
His lodger David Ellis, 40, was arrested in Galway on Friday and is in custody, Garda officers have confirmed.
The arrest comes after police in Wales launched an appeal for information after Mr Warburton disappeared.
Police said Mr Ellis, who had lived with Mr Warburton in Sketty, had stepped off a ferry in Belfast, Northern Ireland, on 6 August.
This prompted a fresh appeal for information which led to Welsh officers being sent across the Irish Sea.
South Wales Police said Mr Warburton's body has not been found but detectives are treating the incident as murder.
Police in south Wales are working with officers in Ireland to extradite a man they want to speak to over the murder of a landlord from Swansea.