The police used tear gas and water cannons to remove the protesters from the city’s main square, the Zocalo.
Striking teachers had been camped out there for weeks. Some responded with petrol bombs as police moved in after a government deadline passed.
The teachers have been demanding changes to education reforms approved by President Enrique Pena Nieto.
The authorities said they wanted to clear the Zocalo for the Independence Day celebrations at the weekend.
Most of the protesters left peacefully by Friday’s deadline. But some stayed on, and police backed by armored vehicles and helicopters clashed with missile-throwing protesters on the square and in nearby streets.
Officers tore down the teachers’ temporary shelters and put out small fires started by the demonstrators and made a number of arrests.
Some of the demonstrators were thought to be radical anti-government activists who were not necessarily associated with the teachers union.
The educations reforms introduced by the government include performance-related tests for teachers.
Critics accuse Mexico’s teachers’ unions of being corrupt and having too much control over job allocation.
Last week, thousands of its members protested outside the Senate in an attempt to disrupt the passing of the bill, which had already been approved by the Chamber of Deputies.
The government has argued that union control over teaching jobs has contributed to corruption, which has seen poorly trained teachers promoted over more qualified colleagues.
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