“The four minors, aged 16 to 17, will appear before a prosecutor today,” a police source told AFP.
The incident allegedly occurred on Sunday in the Moria camp on the island of Lesbos.
Greece is accommodating over 60,000 refugees and migrants stuck in the country after a succession of Balkan and EU states shut their borders earlier this year.
Many of the camps are grossly overpopulated, and rights groups have repeatedly warned that minors must be housed separately for their safety.
There are also regular fights amongst refugees and migrants, who are forced to wait months for their asylum applications to be processed.
Some 5,000 people had to be evacuated from the Moria camp last week when a fire broke out after another brawl.
Greece is in the process of building additional camps on the mainland with EU funds.
But Athens says it has still not received the required EU staff promised by fellow member states to process a massive wave of asylum applications.
This would have enabled Greek authorities to relocate approved refugees out of the congested island camps.
Greece has also bemoaned the failure of fellow member states to accept thousands of refugees from its camps, despite a highly-publicised EU scheme launched last year.
“Fires and incidents in certain island camps are, in a fashion, the result of the failure to share out refugees to all EU member states,” junior foreign minister for European affairs Nikos Xydakis told Die Welt daily on Wednesday, according to an excerpt of the interview sent in advance.
Xydakis said some 7,000 refugees could immediately leave but “most EU states either accept very few or do not even respond to our requests.”
The Greek official also addressed a warning by German interior minister Thomas de Maiziere earlier this month to send migrants back to Greece, ending a five-year suspension of the EU’s Dublin rules, under which refugees must seek asylum in the first EU country they enter.
Xydakis said that returning migrants to Greece under the Dublin regulations is “not realistic” and it would mean the cash-strapped country would end up with an additional one-two million people when it is already “near its limits” with 60,000.