A quarter of inmates at an open prison have developed Covid-19, the Prison Officers Association (POA) said.
More than 100 inmates and 25 staff at HMP Hollesley Bay in Suffolk are ill or off work, it said.
The Ministry of Justice (MoJ) said it had put in place "precautionary measures" at the jail.
"Our priority is to limit the spread of the virus and protect the lives of those who live and work in our prisons," an MoJ spokeswoman said.
Latest government statistics showed the Rendlesham, Orford and Hollesley area had a case rate of 1,030.5 per 100,00 people in the week to 14 January.
The number of cases in the area was up by 77 to 118 in that week. Rates and the number of cases in the wider East Suffolk district fell in the same period.
The MoJ would be "monitoring the situation" at the jail, which has capacity for 485 prisoners.
Jackie Marshall, of the POA, which represents staff, said: "Around the country we've got staff off everywhere and it's proving to be very difficult for some establishments."
She added wardens were trying to look after sick inmates "but we're not trained to do that".
"They're just trying to do the best they can to keep as many people safe, including themselves and their families," she added.
Ms Marshall said the prison service did a really good job in the first wave of coronavirus in March.
"Because the second wave is spreading so fast, they are struggling with it," she said.
Inmates at the jail are normally allowed to spend time outside the prison before release, although current lockdown restrictions prevent this.
This can take the form of daily visits within the local community, weekly with family, or monthly when men can go home for up to four nights.
The POA said there were a smaller number of Covid cases among residents at Warren Hill secure jail, located next to Hollesley Bay.
Highpoint Prison near Newmarket is understood to be coming out of a Covid-19 outbreak, but some 50 staff were still off work due to coronavirus or other conditions, the POA said.
Covid vaccinations for inmates and jail staff in England are expected start rolling out from today according to the POA.