The incident took place at about 6.30am yesterday when a driver burst through the old wooden doors at the College Green entrance.
Gardaí said a number of vehicles in the university grounds were damaged when the car was driven onto the campus and through the locked gates.
The car involved in the incident then drove the wrong way up Dawson St near the college where a number of other cars were damaged.
Gardaí said officers stopped the car on the street. The arrested man was taken to Store Street Garda Station in the city centre for questioning.
A spokeswoman for Trinity said the car drove on to the campus after following a van used by a contract cleaning company that was entering the grounds.
College security staff attempted to stop the car but failed and pursued it as made its way through the front entrance and into the grounds.
The driver then drove back towards the historic front gates of the university which had been closed by the security staff.
No one was injured in the incident.
“However, the driver proceeded to ram into the historic entrance a number of times, succeeding eventually to break through it and causing damage,” the spokeswoman said.
It is understood the car made its way out on to the junction of College Green- Dame St at the front of the college where it then travelled on to Nassau St and the wrong way up Dawson St.
Trinity said the front entrance to the university would remain closed for the rest of yesterday to allow for repairs and it is expected to reopen today.
The damaged front door has been removed.