More than 110 staff at HMP Cardiff are out of work because they either have coronavirus or are self-isolating as contacts of someone who does.
It is believed 113 staff are affected at the category B prison, where around 800 men are held.
Social visits are temporarily suspended at the prison.
The Ministry of Justice said the prison is operating safely and extra support has been brought in.
A Prison Service spokesman said: “Our priority is to limit the spread of the virus and protect the lives of those who live and work in our prisons.
“We have taken precautionary measures at the prison, in line with public health guidance, and will continue to closely monitor the situation.”
The Ministry of Justice would not comment on how many prisoners at HMP Cardiff have coronavirus.
But last week a number of cases at Cardiff Crown Court were adjourned due to defendants who were on remand or awaiting sentencing at the prison testing positive for Covid.
Although specific figures for HMP Cardiff are not available, the number of prisoners testing positive for the virus has increased in prisons in Wales and England - according to the MoJ's own statistics.
At the end of October, 1,529 prisoners had tested positive for Covid-19 since March, an increase of 883 compared with September.
Earlier this month, UK Prisons Minister Lucy Frazer said there had been "significant challenges" but insisted lessons had been learned as the year progressed and "we have taken every opportunity to refine our strategy -and will continue to do so".