Prison staff had checked on the man less than an hour before his body was discovered, shortly before 7pm.

Police were called to the Alexander Maconochie Centre in Hume about 7.30pm Tuesday after ACT Corrective Services officers found the body of a 30-year-old Lyneham man within the centre.

It is being investigated as a death in custody by ACT Policing Criminal Investigations. The death is not being treated as suspicious.

ACT corrective services will also conduct an internal review.

Corrections Minister Shane Rattenbury said the body had been found in a cell in the prison's health centre, but the man had not been in the crisis unit.

Detective Superintendent Brett McCann said the man had been found in the cell, alone, shortly before 7pm.

Corrective Services officers attempted to resuscitate the 30-year-old, but could not revive the man, who had been in custody for about a month.

"There is no indication that there was anything suspicious in relation to the death," he said.

"There were no specified injuries or anything like that."

It is understood Corrective Services officers checked on the man less than an hour before his body was found.

Mr Rattenbury told a press conference on Wednesday the 30-year-old's name would not be released at the request of the family.

He said the incident was being investigated as a death in custody by ACT Policing criminal investigations and a report was being prepared for the ACT coroner.

"On behalf of the ACT Government I would like to express my deepest sympathy to the family and friends of the individual," Mr Rattenbury said.

"This will be a difficult time for them and I do ask that their privacy is respected."

He said correctional and health staff were being offered support, as well as detainees.

Mr Rattenbury said he believed the prisoner was on remand, but did not disclose what offence he had been charged with.

Justice and Community Safety Directorate spokeswoman later confirmed the man had been on remand.

Detective Superintendent McCann said investigators were looking at possible underlying health issues for the man, but could not confirm whether he had been waiting for a transfer to the mental health unit.

The next-of-kin of the deceased has been notified of the death, which Detective Superintendent McCann described as "tragic".

He said a forensics examination had been conducted on Tuesday evening and a post mortem was to be conducted on Friday as part of preparing a coronial brief for the ACT Coroner.

"The brief will be ongoing," he said.

"It'll be presented to the coroner in a couple of months' time."

A Justice and Community Safety Directorate spokeswoman said excluding the most recent incident, there has only been one death in custody at the Alexander Maconochie Centre.

“Since the AMC began receiving detainees in March 2009, one detainee has passed away while in custody at the facility,” she said.

“The detainee passed away from natural causes.”

Between July 1979 and June 2011, a total of five deaths of individuals in ACT Corrective Services’ custody have occurred, she added.