Police were notified that damage had been sustained at the clocktower and it was locked down as a precaution on Wednesday, a spokeswoman said.
"One person has been arrested in relation to the incident and charges will be considered," the spokeswoman said.
Protester Rosie Cruickshank said the group wanted university to "make a stand about the genocide in Gaza" and support the BDS movement.
"We were staging a peaceful protest outside and we entered the clocktower - as many students have done before us - but we have been removed now and one person was arrested for wilful damage."
University of Otago Vice-Chancellor Grant Robertson said it was "important that students and staff are able to express their views and protest within the law".
"However, there is no place for vandalism or disorderly actions, particularly when the safety of others including staff and students is put at risk.
"This protest crossed that line. This is against the kaupapa of our community and is not welcome."