A spokesman for the police in Sao Paulo, home to some 20 million people, said only that "there were fatalities, but we cannot yet confirm the number."
The security chief for Sao Paulo state was due to speak later. A spokesman for his office said the attacks were "unusual."
According to Brazilian press reports, the shootings took place in 10 places in the Osasco area, with two more attacks in Barueri -- all in a period of about two and a half hours. G1 news site said a total of 23 people died.
The mayor of Osasco, Jorge Lapas, said video footage supports a theory that the killings could have been reprisals for the earlier death of a police officer.
"We want to take measures so that the situation does not worsen over the coming days," he said.