There has been an outbreak of coronavirus at The Mount prison at Bovingdon near Hemel Hempstead.
Positive cases were found during routine tests earlier this month.
The latest Covid-19 figures for the Bovingdon and Chipperfield area, which include the jail, showed a jump of more than 100 cases to 222.
A spokesperson said: “Testing at HMP Mount has led to a number of coronavirus cases being identified, but robust safeguards are in place to reduce the spread of the virus.”
On its website the prison said: “Prison visits are temporarily suspended at The Mount following local restriction tiers. We will update here as soon as this changes. There may be the opportunity for visits under exceptional compassionate reasons which should be agreed in advance with the prison prior to travel.”