It is understood a number of health workers who attend the jail have tested positive for Covid-19.
So far, two prison staff and two inmates are self-isolating as a precaution while they await test results.
Magilligan is a medium-security jail housing around 450 male inmates.
In a statement, the Prison Service said: “We can confirm a number of people from a partner organisation have tested positive for Covid-19.
“The service has well-established track and trace processes in place and these have been instigated.
“As a consequence, in-person visits at Magilligan have also been temporarily suspended.
“The safety of everyone at Magilligan remains our primary focus.”
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