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."

It said the step was "inflammatory and inappropriate".
Railways Minister Ghulam Ahmad Bilour made the offer after a wave of protests against the film across Pakistan and the wider Muslim world.
Dozens have died in clashes between police and protesters in Pakistan and countries such as Tunisia and Sudan.
Sunday saw a fresh round of protests over the film in Pakistan, Nigeria, Greece and Turkey.
Most passed off peacefully, but in the Greek capital Athens, riot police and demonstrators clashed. Six people were arrested.
A state department official told the BBC: "The president and secretary of state have both said the video at the core of this is offensive, disgusting, and reprehensible - but that is no justification for violence, and it is important for responsible leaders to stand up and speak out against violence.
"Therefore we find Mr Bilour's announcement is inflammatory and inappropriate.  We note that the prime minister's office has dissociated itself from his comments."
The exact origins of Innocence of Muslims, the low-budget film that has prompted the unrest, are unclear.
The alleged producer of the trailer of the film, Nakoula Basseley Nakoula, is in hiding.
Anti-US sentiment grew after a trailer for the film dubbed into Arabic was released on YouTube earlier this month.
US citizens have been urged not to travel to Pakistan, and the US embassy has paid for adverts on Pakistani TV showing President Barack Obama and Secretary of State Hillary Clinton condemning the film.
Although US targets have borne the brunt of protests against the film, anti-Western sentiment has been stoked further by caricatures of the Prophet Muhammad published this week in the satirical French magazine, Charlie Hebdo.
France shut embassies and other missions in about 20 countries across the Muslim world on Friday.
An 18-year-old man who threatened the magazine's editors on Facebook has been charged with terrorism-related activity  following his arrest in the southern French city of Toulon, a  judicial source told AFP news agency on Sunday.

4 June 2014 Last updated at 21:59 BST
The government is so concerned about the lack of cover that it is introducing a new scheme that will force insurers to offer policies at affordable rates.
But that doesn't come in until next year.
Clinton Rogers reports from the village of Moorland.
Two men have been arrested by police in connection with a disturbance in Chambers Street in Edinburgh.
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The US state department has condemned a Pakistani minister's offer of $100,000 (Â£61,600) for the death of the American maker of an anti-Islam film.
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