Prisoners in HMP Winchester fear they have been given a "death sentence" due to coronavirus, an inmate's partner has said.
She said the prisoners were being kept in kept in their cells for 23 hours a day and were concerned about infection being brought in.
The BBC has been told there has been one case of Covid-19 in the jail.
The Prison Service said it had enacted "robust and flexible plans" for jails.
The woman, who wished to remain anonymous, said she and the families of other prisoners she had spoken to were "terrified".
"[The prisoners'] key concern is that they're on a death sentence - they know once it's in a prison it will be rife.
"It will go everywhere because there is not enough room to self-isolate even though they're sat in their cells. Officers still come and go from those cells, work parties still go in communal areas, they still have to go for their meals.
"They could die in there. I'm not exaggerating. They could die if they got that virus," she said.
She also said the quality of food had deteriorated because of staff shortages.
It is believed the inmate with Covid-19 caught the virus outside the Category B prison, was subsequently arrested and sent to jail on remand.
The government announced earlier this week that up to 4,000 prisoners in England and Wales are to be released in an effort to control the spread of coronavirus.
A Prison Service spokesperson said: "We have robust and flexible plans in place to protect prison staff, the public and prisoners, based on the latest advice from Public Health England.
"Personal protective equipment is being provided to officers and all prisons have the soap and cleaning materials they need."
The Ministry of Justice said, as of Tuesday, 129 prisoners had tested positive for Covid-19 across 47 prisons.
Ten inmates with coronavirus have died, the ministry said.
Twenty-four prison staff have also tested positive, as have five escort and custody staff.
Two staff members at Pentonville Prison in north London died after showing symptoms of coronavirus.