Officers said the 24-year-old, who was being treated at a Dublin hospital with mental health problems, has been released from medical care.
He is held at Terenure Garda Station where he is detained under section four of the Criminal Justice Act.
Michael Hughes died from multiple stab wounds after a frenzied attack at Manor Villas complex, near Mount Argus Church, Harold’s Cross, on Saturday morning.
It is believed he was stabbed repeatedly with a pair of garden shears.
It was later claimed the suspect, who was arrested at the scene, presented himself at two hospitals seeking mental health assistance in the days prior to the attack.
The Health Service Executive said it was helping gardaí with its inquiries.
Mr Hughes, of Banagher, Co Offaly, was at a friend’s engagement party in Dublin on Friday night and was returning to stay at his cousin’s flat when he was attacked.
His parents, Liam and Mary Hughes, said although they heard reports of the fatal attack they were unaware their son was the victim until more than 12 hours after his death. His body has not yet been released and no funeral arrangements have been made.
A CIÉ employee, Mr Hughes got engaged to his girlfriend Deborah Lynch in October.