The death occurred shortly after 5:30am, after Gardaí and emergency services were alerted by prison authorities to an incident within the facility.
A man in his 40s was injured during the incident and received treatment from emergency services, however, he was pronounced dead a short time later.
The scene remains preserved for a full forensic and technical examination.
The victim was arrested in August after a firearm was seized in south Dublin, and a kilogram of cannabis herb, worth an estimated €20,000 was also seized.
He was subsequently charged with drugs and firearms offences and was on remand in Cloverhill awaiting trial when the attack took place this morning.
The coroner has been notified and the services of the State Pathologist and Garda Technical Bureau have been requested.
