The staff are based at the Hydebank Wood (HBW) facility for women and young offenders in south Belfast.
The Northern Ireland Prison Service said a further 14 staff who tested negative are self-isolating and two prisoners have also been put into isolation.
A spokesman said: “The prison service has well-established and embedded arrangements for testing staff, and to track and trace close contacts following a positive case.
“Following the contact tracing at HBW, a further 14 staff, who have all tested negative, are self-isolating and two prisoners have also been put into isolation as a precaution.
“The safety of staff and the people in our care is our priority and the prison service will take all necessary steps to mitigate against the risk of Covid-19 in our prisons.”
Prison visits were temporarily suspended on Friday as Northern Ireland came under tough new restrictions aimed at stemming the spread of coronavirus.
There has been a marked increase in the number of new cases of the virus in the region, with hospital admissions also starting to rise.
Some 1,031 new Covid-19 cases were reported in Northern Ireland on Saturday by the Department of Health, part of the 6,891 positive cases notified in the last seven days.
Two further deaths were also reported, taking the toll recorded by the department to 610.
As of Saturday, there were 231 patients with Covid-19 being treated in hospital, with 27 in intensive care.
