The demonstrators belong to an anti-capitalist group calling itself the Black Bloc.
The newspaper Folha said 120 people were arrested in Rio and 56 in Sao Paulo, although police gave no official number.
The clashes in Rio came after a march by 7,000 people as part of a two-month-old strike by teachers seeking salary hikes.
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Protesters hurled homemade explosive devices and tore metal shutters from buildings to use as shields against police firing tear gas.
The demonstrators also set fire to a police car and a bus.
A week ago another march in support of the striking teachers also degenerated into clashes with police.
