Part of Elmley Prison on the Isle of Sheppey has been isolated after two officers and two prisoners tested positive for coronavirus.
A Prison Service spokesman said: "Movement has been restricted in one house block as a precaution after two officers and two prisoners tested positive for Covid-19.”
Inmates in the affected area - one of six cell blocks on the site at Eastchurch used to hold prisoners on remand - are unable to use video link facilities so they cannot make appearances in court or talk to family members.
Five members of HMP Elmley staff are also self-isolating.
Five staff members at neighbouring HMP Swaleside have tested positive for coronavirus but these cases are not thought to have been transferred within the jail.
The spokesman added: "Prisons operate under a national framework which sets out how restrictions are managed.
"We continue to monitor the situation across the estate.
"Should restrictions need to be re-imposed to ensure the safety of staff and service users, we will not hesitate to do this."