Tyler Sweeney of the Miramichi area has been identified as the inmate who died at the Southeast Regional Correctional Centre last week, according to the Department of Justice and Public Safety.
RCMP investigated Sweeney's death and ruled out foul play, said Cpl. Gabriel Deveau of the Shediac detachment.
Staff found the 49-year-old man unresponsive in his cell Thursday.
Paramedics tried to resuscitate Sweeney, but he died at 6:35 p.m., the Justice Department said Monday.
A department release said "initial indications are that the death is attributable to natural causes."
Deveau said Sweeney had a "medical history" and heart issues.
Department spokeswoman Danielle Elliott said in an email that Sweeney was on remand at the jail and that the province had no other comment.
A coroner's investigation continues.