The man was pronounced dead at about 19:00 GMT on Wednesday at HMP Swaleside, on the Isle of Sheppey. It is believed he was stabbed to death.
Two men, aged 32 and 44, have been arrested on suspicion of murder and remain in police custody.
HMP Swaleside is a category B prison and holds about 1,100 inmates.
A murder investigation has been launched after an inmate was found dead at a prison in Kent.