The incident happened earlier outside an Edinburgh University building where a student occupation is underway.
A report will be sent to the procurator fiscal. It follows footage posted on social media showing an altercation between a security guard and a student.
The university said it "deeply regretted the unfortunate incident".
About 30 students have been occupying a university building in protest at its "failure to commit" to divestment from fossil fuels.
Eric Lai, one of the occupiers inside, said: "We have been repeatedly told that the university supports our right to protest, but that couldn't feel further from the truth."
"The university have posted dozens of guards to the doors, and have now taken to intimidation and violence to shut us up. It is hard to imagine a more inappropriate way to handle student protest."
"The university need to immediately change their approach, allowing open access to the building and engaging with the politics of why we're here, rather than just covering their ears to both the demands of students and staff, and the desperate urgency of tackling climate change.
"Until they move their money out of fossil fuels, we're going nowhere."
An Edinburgh University spokesman said: "The university is aware of, and deeply regrets, the unfortunate incident that is currently being played on social media.  The matter is now in the hands of the police.
"We continue to support the right of students to peacefully and lawfully demonstrate and the University is using private security outside its buildings in Chambers Street in order to secure the safety of staff and students during the occupation."
"We are constantly reviewing our security arrangements to make sure that they are appropriate to the circumstances in what is an evolving situation."
Two men have been arrested by police in connection with a disturbance in Chambers Street in Edinburgh.