The officers are in quarantine as a precaution while contact-tracing takes place, and their roles are being covered by staff who are not impacted by the positive case.
The government says that no inmates have been affected and there is no evidence that the virus is present in the prison.
As a precaution, all social visits have been suspended for prisoners.
During this time, prisoners will be able to undertake video calls with their family members, following the installation of terminals in March. Prisoners can also contact their family members by using their in-cell phones.
Nick Watkins, acting governor, said: 'These measures are vital to protect the health of our staff and prisoners, and to ensure that we are all playing our part to minimise the spread of Covid-19. We have well-prepared plans to deal with the absence of staff in a scenario such as this.
'We are keeping the Independent Prison Monitoring Board informed of all measures we are taking to look after the well-being of prisoners and our staff.'