He is the second prisoner to die at HMP Littlehey in Cambridgeshire with the virus.
This occurs after another prisoner died in hospital on Saturday after contracting Covid-19.
The 66-year-old man, who was already receiving end-of-life care, was serving a sentence at HMP Manchester, confirmed the prison service.
The terminally ill detainee had an underlying condition before he tested positive, authorities said.
The first viral prisoner to die is an 84-year-old man who was also detained in Littlehey at the hospital on March 22.
After the death of the detainee, named sources said he was convicted of the pedophile Edwin Hillier.
A prison service spokesperson told Mirror Online: “An 84-year-old prisoner at HMP Littlehey died in hospital on March 22. Our thoughts are with his family right now.
“As with all deaths in detention, an independent investigation will be conducted by the Prison and Probation Ombudsman.”
Over the weekend, 19 prisoners had tested positive for Covid-19 in 10 British prisons and four prison staff had tested positive for the disease in four prisons.
Three members of the escort and custody staff also tested positive for Covid-19.
The prison service said solid contingency plans had been put in place at its facilities in consultation with Public Health England and the Department of Health and Welfare.
He added that prisons are well prepared to take immediate action whenever suspected or suspected cases of Covid-19 are identified, including the isolation of people if necessary.