Masked protesters fought pitched battles in the city center with police who fired water cannon and tear gas much like the scene in London this week.
Students say the current system is under-funded and unequal even though President Sebastian Pinera has pledged extra funding.
The demonstration began peacefully with tens of thousands of students and teachers marching through Santiago and elsewhere in Chile. But masked protesters then split off from the main crowd and began clashing with police.
Students are calling for a national referendum on their demands
Deputy Interior Minister Rodrigo Ubilla said at least 273 protesters had been arrested nationwide, and 23 police officers had been injured in Santiago.