West Mercia Police said it received a report from HMP Stoke Heath in Shropshire that a man in his 40s had been found dead at about 7.40am yesterday.
A 26-year-old man was arrested in connection with the incident after officers attended the prison, and he remains in custody.
Superintendent Carl Moore said: “Our thoughts are with the family of the man who has lost his life.
“An investigation has begun to establish the full circumstances of his death.”
HMP Stoke Heath is a men’s Category C prison that houses nearly 800 inmates.
In its last unannounced inspection in 2023, it was given the highest rating for keeping prisoners safe by HM Inspectorate of Prisons.