A number of students, including women, and two journalists were injured in a police crackdown at the Banaras Hindu University (BHU) during a protest on Saturday night over the incident.
"A committee has been constituted under the chief secretary. Necessary action will be taken on the basis of its report. The committee will see as to how the police had behaved and examine other aspects," he said.
Mr Naik was responding to queries from reporters in Lucknow about the incident.
The governor described the incident as sad. Chief Minister Yogi Adityanath has already ordered a probe into the incident.
In the wake of the violence, the university has advanced the puja holidays from Tuesday till October 2. Earlier, the holidays were to have started from September 28.
Violence erupted after some students, protesting against the alleged sexual harassment incident of Thursday, wanted to meet the Vice Chancellor at his residence on Saturday night, according to police and university sources.
A BHU spokesperson said some students wanted to "forcibly" enter the Vice Chancellor's residence but they were stopped by the security guards of the university.
Subsequently, there was stone-throwing by "outsiders" who had joined the students.
Police then used batons to control the situation.