The suit was filed in a federal court in the central-west state of Goias.
Brazil has asked for the “immediate suspension of all accounts that give information about the location of police radar,” the office of the Attorney General of the Union, said in a statement.
The government wants “the definitive closure of accounts revealing the date, time and place of police checkpoints,” the statement said.
The lawsuit also orders Twitter to pay 500,000 reals ($290,000; £183,000) for each day that it does not comply with the request.
Twitter is not commenting on the case.