Matthew Healy was subject to the attack at Mercy University Hospital (MUH) in the early hours of Sunday.
The suspect, in his 30s, was previously involved in a crime in which an elderly woman was terrorised.
He received a suspended sentence for his role in this incident.
It is understood that a decision to either charge or release the suspect will be made later today.
Gardaí are not looking for anyone else in the case.
Officers are investigating whether an issue over noise triggered the fatal attack by an agitated younger patient in a Cork hospital.
Separate investigations are now under way by gardaí and MUH into the fatal incident shortly after 5am yesterday on one of the main wards in the Cork city centre hospital.
The deceased has been named locally as Matthew Healy, from Berrings in Co Cork.
Mr Healy’s wife, Delia, died after a short illness on January 2. The couple lost a daughter in an accident decades ago.MUH triggered its emergency response plan while gardaí sealed off part of the hospital where the attack occurred yesterday.
Other patients and staff raised the alarm when they discovered the elderly patient with critical injuries at around 5am on one of the main MUH wards.
A man in his 30s was discovered in a highly agitated state at the scene and was restrained until gardaí arrived.
No weapon is believed to have been involved in the incident. However, investigators are looking into the possibility that the deceased man hit his head against a walking frame during the incident.
The aftermath was witnessed by several other patients and MUH staff members.
It is unclear what triggered the fatal attack but gardaí are investigating if there was a dispute or argument between the two men.
The man in custody will be given a full medical and psychiatric evaluation.
Father-of-four Mr Healy was not previously known to the man in custody.
The men come from different parts of Cork.
Gardaí are investigating whether the younger man may have been in a disturbed or agitated state in the minutes before the incident.
The incident occurred in the main section of the city centre hospital which is one of Ireland’s oldest and best known acute teaching hospitals outside Dublin.
Security staff and gardaí were alerted when the pensioner was discovered critically injured and the scene was immediately sealed off.
Desperate efforts were launched to assist the elderly man on the ward.
However, Mr Healy was pronounced dead a short time afterwards.
A full forensic and technical examination will now be conducted of the scene.
The man’s remains were transferred to Cork Morgue for a post-mortem examination, which was completed last night.
A separate investigation by MUH into the incident is now under way.
In a statement, MUH confirmed it was providing counselling and support services for those affected.
“MUH can confirm that gardaí are investigating a fatal incident involving a man in his late 80s at the hospital early this morning,” a spokesperson said.
“The hospital is providing counselling services to patients and staff affected by the incident,” it said.
“MUH management and staff are saddened and shocked at the tragic and unexpected death of an elderly patient in an incident at the hospital and express their deepest condolences to the family, relatives and friends. May he rest in peace.”
A garda statement meanwhile said: “A man in his 30s was arrested at the scene by investigating gardaí and taken to Bridewell garda station, Cork, where he is currently detained under Section 4 of the Criminal Justice Act, 1984.”
The man can be detained for questioning for up to 24 hours.
“The scene is currently preserved for forensic and technical examination,” the statement went on.
“An incident room has been established at the Bridewell garda station and the services of the State Pathologist have been requested.”
“A Garda Family Liaison Officer (FLO) has been appointed in the case and the family of the deceased have been notified.”
“Investigating gardaí are not currently seeking anyone else in relation to this incident.
“No further information or garda spokesperson is available at this time.”
Cork County Council member Michael Looney said the deceased man was a “pure gentleman”.
He knew Mr Healy from Berrings, about 20km north-west of Cork city, and the Healy family is very highly respected locally, he said.
“He was a very quiet man. The last place you would think something like this would happen is in a hospital,” Mr Looney said.
“When you go in to hospital you think you are safe in your bed.
“The people of Berrings are devastated. The family are here for generations. They are hugely respected.”
“They are lovely people and he (Mr Healy) was a thorough gentleman. A pure gentleman.
“His wife is only dead a few weeks.”
Elderly-rights campaigner Paddy O’Brien said he was deeply shocked by the incident and extended his sympathy to everyone involved.
“I sympathise with the family of the man involved in this tragedy,” he said.
“For a man to go into hospital only to lose his life – I just don’t know what to say. The Mercy is a fine hospital…But this is an awful, desperate tragedy.
“That poor man went into hospital with some illness and nobody could expect a tragedy like this to happen.”