Police have been notified and are responsible for notifying the man's next of kin, Harrex said.
"Our thoughts are with the man's family and friends. Other men in the unit and staff are being provided with support," she said.
All deaths in custody are referred to the coroner for investigation and determination of cause of death.
An investigation by the independent Corrections Inspectorate will also be carried out.
A source told the Herald that the man had been having trouble breathing and had been asking for medical assistance for weeks.
Today, however, Corrections said they were unable to answer specific questions from the Herald.
"As the man's death remains subject to investigation, and the coroner is yet to determine the cause, we are limited in the amount of detail that we are able to provide," Harrex said.
Police were not investigating, a spokeswoman said, referring enquiries to Corrections and the coroner.
A spokeswoman for the coroner confirmed the man's death has been reported to them.
"However, because the inquiry is at an early stage, no further information is available," she added.