The men, in their 30s, are thought to have sustained blows to the head during the assault, which according to local media reports was carried out with a hammer.
Police in Melbourne arrested a suspect three hours after the incident which occurred at about 1am local time at a boarding house in Lynedoch Avenue, in the St Kilda East area of the city.
Their alleged 31-year-old attacker also sustained injuries and was found at the same hospital where the two victims were being treated.
Police initially said the backpackers had suffered life -threatening injuries. Later a statement was released saying both Irishmen were in a critical but stable condition in the city’s Alfred hospital.
“Police arrested a third man at the Alfred, where he was being treated for non life-threatening injuries, around 4.30am,” said a police spokeswoman. “He remains under armed guard at the hospital.”
The Department of Foreign Affairs is providing consular assistance to the men’s families.
Meanwhile, an Irishman is recovering in hospital after he was injured in a shooting in Spain.
The victim, believed to be a Dubliner in his late 20s, was shot in a bar in Torremolinos, on the Costa Del Sol, on Saturday night.
It is understood he has a number of previous convictions and is known to gardaí.
The Department of Foreign Affairs said it was aware of the incident but consular assistance had not been requested.
Earlier this month, Irish teenager Martin Murphy was hospitalised after being attacked in the Spanish holiday resort of Benidorm.