The incident occurred at the Rathmore Rd jail overnight on Wednesday, just months after the new €43m purpose-built facility became operational.
Prison authorities said it appeared as if a stop-cock in a roof-top water tank malfunctioned, sending water cascading into the school area, and leaving about an inch of water swirling on the floor area.
A spokesman for the Irish Prison Service (IPS) said the school is likely to remain closed until next Monday to facilitate repairs.
Builders were on site yesterday assessing the damage and making repair plans.
The IPS spokesman said it was too early to assess the cost of the damage, but he said the nature of the materials used in the area should make it relatively easy to repair quickly.
About 160 inmates were transferred last February from the Victorian-era former prison to the new facility built nearby.