Soon after a peaceful march by more than 5,000 people ended in Rio, a much smaller masked group attacked shops, set fire to a police car and threw petrol bombs.
There were also clashes in Sao Paulo, where shops were ransacked.
Police responded with tear and pepper gas and detained dozens of people.
Four officers were injured and seven banks were vandalized during the unrest in Sao Paulo, according to Reuters news agency.
Extra police had been deployed in Rio de Janeiro for the huge protest coinciding with Teacher’s Day, on which the country recognizes the profession.
Many shops and banks had boarded up their windows after last week’s larger protests, which had gathered more than 10,000 supporters.
Police also cordoned off the Rio house of representatives, which was targeted last week.
After the end of Tuesday’s march, masked protesters from the so-called Black Bloc anarchist group set fire to the boards, as well as public telephones, rubbish bags and other street furniture.
Metal boards were also taken by some groups and used as shields to confront the police.
A police car was set alight and protest slogans written on walls.
Teachers in Rio are demanding better working conditions and salaries and have the support of colleagues in other cities.
They have been on strike for two months and many complained that Rio’s state government had started procedures to sanction the striking teachers.
On Tuesday night, a Supreme Court judge said it considered the government’s actions illegal.
Judge Luiz Fux told Brazil’s state news agency, Agencia Brasil, that the sanctions infringed, “even if in a roundabout way, the civil servants’ right to freedom of expressions through strike”.
Luiz Fux also summoned union leaders and government officials for talks on October 22.
In an earlier demonstration on Tuesday, a group of homeless people tried to break into the house of representatives of Sao Paulo.
Police held off the crowd, and a small group later met with government officials.
In the south-eastern city of Belo Horizonte, a peaceful protest was held a central square.
Smaller groups also gathered on Tuesday in Brasilia, the north-eastern city of Salvador and other cities.
Brazil’s security situation is a challenge to cities that will play host to the 2014 World Cup and 2016 Olympic Games.
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