The investigations will focus on the reasons for the disturbance and the manner in which it was handled.
Just after 4pm yesterday afternoon about 70 prisoners barricaded themselves into a recreation room in the D Wing of Mountjoy Prison.
Senior management, and the prison's governor John Lonergan were called in to attempt negotiations.
After a stand-off that lasted about two hours, some 100 prison guards in riot gear stormed the area and restored control.
Five prison officers were injured in the incident. One officer had his teeth knocked out. Two prisoners suffered minor injuries.
The exact reasons for the protest are not yet known, but prisoners are believed to be angry at new security arrangements in the prison, and a clampdown on efforts to smuggle mobile phones, drugs and other prohibited items into the prison.
A Garda investigation has been launched into all aspects of the assaults, and other criminal damage, while the prison authorities are examining the cause of the protest and how it was handled.
