It is understood the students were out celebrating their annual Christmas event when the arrests were made.
Most of the arrests took place in the city centre, Lismore Park and Templars Hall housing estates.
All students have since been released.
Gardaí say they will be talking to authorities at Waterford Institute of Technology in relation to the matter.
WIT and the WIT Students' Union have said they had no role in organising the day's events.
