Physical visits to the prison have not been stopped amid the outbreak, and video visits also remain in operation.
In a statement, a spokesperson for the Irish Prison Service said they are working closely with Public Health and The HSE.
“At all points, Outbreak Control Teams (OCT) are guided by advice from local Public Health clinicians and meetings with Public Health are convened at regular intervals throughout the course of each outbreak.”
At Mountjoy, 22 prisoners from C & D Divisions in have tested positive for Covid-19.
Seven prisoners from C Division in Portlaoise Prison and at Midlands Prison, 1 prisoner from G Division have also have confirmed cases.