Youths backed by the extreme right-wing group Golden Dawn entered a vocational high school in Thessaloniki, Greece, on Wednesday and hurled gasoline bombs, flares and rocks at a rival gathering.
Left-wing university student groups had been demonstrating at the school against government education reforms.
Police officers used tear gas to break up the violent demonstration as classes continued at the school in the area of Stavroupoli.
A youth wing of the extreme right group Golden Dawn had earlier expressed support for the counter-demonstration.
Dozens of others were initially detained after the violence, Greek police said in a statement.
"A total of forty individuals were brought in, of which six were arrested and cases were filed against them for violating the legislation on weapons."
"Police forces, which were deployed at the scene, intervened immediately and prevented further escalation of the situation."
A Greek court ruled last year that the Golden Dawn party was operating as a criminal organisation, and sentenced members of its leadership including former lawmakers to up to 13 years in prison.