Neil Anthony Davey, a former Victoria College pupil who was born in the Island, was found dead at lunchtime on Saturday.
He was being held on remand.
In September last year he was jailed for two years for importing heroin into Jersey by post.
At the time of the Royal Court sentencing he was described as a drug addict.
Prison governor Steve Guy-Gibbens said that staff who found Davey immediately cut him down and tried to resuscitate him, and despite an ambulance attending he was pronounced dead at the General Hospital a short time later.
Mr Guy-Gibbens has ordered an internal inquiry, and Deputy Viscount Peter de Gruchy has begun the formal inquiry ahead of the opening of an inquest.
Home Affairs Minister Wendy Kinnard and the chairman of the Board of Visitors, Jurat John Tibbo, have visited the La Moye prison to talk to the governor and staff.
