Australian police have arrested a 49-year-old man over a stabbing rampage at a secure psychiatric hospital which left two patients dead, they said on Thursday.

The man is being held after reportedly attacking his room-mate with a kitchen knife at the hospital in Melbourne late on Wednesday, before turning on another patient who was lying in bed.

Police were applying for court permission to interview the suspect.

They said a 54-year-old victim was stabbed several times in the upper body while the body of the second man, 36, was found nearby at the low-security centre. The motive for the attack was unknown.

"It's my understanding that both the victims and offender were in the facility after committing the offence of murder," Detective Sergeant Wayne Cheesman told reporters.

"I know the room-mate and the offender were considered quite friendly," he added. "They would often go out on day pass and leave and go fishing together, and what brought on the altercation, we don't know."

Melbourne's 118-bed Thomas Embling Hospital was purpose-built to house patients referred by the criminal justice system.