The prisoner was found injured critically late Thursday night in his cell and taken to hospital where he succumbed to his wounds after one day, reported the national broadcaster YLE.
The incident is not being investigated as a crime, but the KRP is investigating the death, said the police.
Earlier, on Thursday the prisoner attacked a police official when the officer went to interrogate him in the custody.
The police officer is reported to have been seriously assaulted during the interrogation and taken to hospital.
Since the police officer was on official duty at the time of the incident, the case was being investigated as attempted murder.
The interrogating officer is a sergeant at the Helsinki Police Department.