Senior Sergeant Anthony Bond, of Dunedin, said officers were called to Dunedin North Intermediate School about 1pm after a man entered the school grounds and stripped off all his clothes.
Four officers responded and worked to apprehend the man.
The man was believed to have been intoxicated, with a combination of drugs which appeared to have affected his state of mind, Snr Sgt Bond said.
He was arrested for performing an indecent act and was given a blanket to wear by officers.
Investigations were ongoing to determine the extent of what the man had done, and the extent of charges were being considered.
Another arrest was made on Castle St, of a person throwing a bottle.
A police spokeswoman also said officers were called to reports of a disorder incident in Butts Rd about 3pm, involving people walking in the street and behaving in a vaguely threatening manner.
Earlier, the University of Otago Proctor said St Patrick's Day was a "big challenge" as the student quarter in North Dunedin.
"Our priority today is safety, for the students and the public. The day is a big challenge for the University, the DCC, FENZ and the public," proctor Dave Scott said.
While partying students have been on rooftops and police have been called to reports of early-morning bottle throwing and a couch fire, up to 1000 students have gathered at Brackens View, a green space above Logan Park.
Mr Scott endorsed their choice of location.
"This is as good as it gets, its much easier to clean up, although we'll need a 'dads' army' tomorrow to get it done. We acknowledge that it's not ideal, but if not here, where? We've had students running across the state highway and in public areas.
"We're encouraging young people not to be on roofs and we're educating them as we go.
Earlier, a Fire and Emergency New Zealand spokesman said a crew from Lookout Point station responded to reports of a couch fire in Leith St about 8.45am.
A hose reel was used to extinguish the fire and police were also called to attend, the spokesman said.
A police spokesman said officers were called to reports of bottles being thrown at the intersection of Forth St and Union St East about 7.45am.
Students have been seen on rooftops despite police warnings that such behaviour was unsafe and may result in arrests.
