The strike takes place less than a month before the beginning of the football World Cup, in another hiccup in preparations for the event.
The industrial action affects several World Cup host cities, including Sao Paulo, where the tournament will begin on 12 June, and Rio de Janeiro.
The authorities were quick to play down any risk of major disruption.
Only civil police, who deal with criminal enquiries, are taking strike action.
They area demanding a pay rise of up to 80%.
“There is no climate for a general [police] strike now in Rio de Janeiro,” said Brazil’s Big Events Secretary Roberto Alzir.
“Even if that was to go ahead, we would be prepared for that,” he added.
Brazil’s preparations for the event have been criticised by World Cup organisers, Fifa. All the stadiums should have been ready in December, but some were still being finished earlier this month.
The final match will be played in Rio de Janeiro’s Maracana stadium on 13 July.
Earlier the authorities in Rio announced the city’s security plans for the World Cup.
Up to 20,000 people, including military police and soldiers, will be used to guarantee safety in the city during the event.
The announcement follows concerns about the increase in drug-related violence in Rio’s poorest areas in recent months.
Police had launched a much-praised “pacification” plan in the city’s notorious shanty towns, or favelas.
But the deaths of residents in clashes with police in the past month led to protests and calls for the incidents to be fully investigated.
A Freelance Journalist, Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A contributory writer for Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
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