Violence broke out as the demonstration wound down Tuesday afternoon, with hooded vandals attacking police, The Santiago Times reported.
The crowd of protesters was estimated at 50,000 by police and as high as 200,000 by an official of a teachers union that took part in the demonstrations.
Student protesters were seeking government action for "profit-free" education, while teachers were demanding higher pay and pensions.
The huge crowd was mostly peaceful, police said, until "encapuchados," or hooded vandals, attacked police, throwing furniture, stones and slabs of pavement.
Police responded with tear gas and rubber bullets.
Some 13 officers were injured, two seriously, said police chief Luis Valdes.
At least 200 people were arrested.
Both legs of a 15-year-old boy were reportedly broken when a police man tried to remove the boy's hands from a bridge he was clinging to at the protest scene. Unofficial reports said the boy fell onto concrete below and broke his legs.