Alan Averill suffered a chest wound during an incident at Stoke Heath Young Offenders' Institution near Market Drayton, Shropshire. He was airlifted to hospital, but died later.
A Prison Service spokesman said another prisoner had been put into segregation following the stabbing and police were investigating the incident.
"Mr Averill was in a cookery lesson when he was found to have suffered a chest wound.
"It is understood that some form of weapon was used to cause that injury," the spokesman said. In April, Wolverhampton Crown Court sentenced Averill, from Wolverhampton, to a 12-month term for burglary, taking and driving away.
The coroner has been informed about his death.
Inquest, an organisation which has monitored deaths in prison and police custody since 1981, said the killing was the only such death in a young offenders' institution that it was aware of.
Nick Flynn, of the Prison Reform Trust, said the tragedy added to a picture of growing levels of violence being experienced by young prisoners. "The Chief Inspector of Prisons has identified bullying and violence as major issues to be dealt with at all YOIs and the fact that somebody has now died at one perhaps shows that the problems are worse than the chief inspector initially envisaged."
A record 70 prisoners took their own lives in prisons last year, but homicides remain comparatively rare, at a rate of around one a year.
t Approximately 20,000 television sets are to be ordered for cells over the next three to five years, Joyce Quin, the prisons minister, disclosed in a Commons written reply last night.Reuse content