An inmate at Matsqui Institution in Abbotsford was pronounced dead in hospital on Wednesday evening.
Assistant warden Heather Kelly said Christopher Robert Roy, 38, was found unresponsive in his cell on Monday.
Staff members immediately began performing CPR, and emergency services were called.
Roy was taken to Abbotsford Regional Hospital, where he died two days later.
At the time of his death, Roy was serving a two-year sentence for break and enter and breaches of his probation and bail conditions.
His next of kin have been notified of his death.
Kelly said as in all cases involving the death of an inmate, the police and the coroner have been notified, and Correctional Service Canada will review the circumstances.