There are 407 prisoners in the jail, which is one of the biggest in the country.
About 40 inmates in Cloverhill Prison in Dublin are being tested for Covid-19, as they have symptoms of the virus.
So far one prisoner has tested positive, and the rest are waiting for their results.
The Irish Prison Service says all staff and inmates will now be tested, as it manages the outbreak.
There are 407 prisoners in the jail, which is one of the biggest in the country.