Press reports put the death toll at 13, but a police spokesman told AFP that only 10 deaths have been confirmed so far.
"We have not established whether these deaths are related. All we know for now is that they occurred in the same area of Campinas," Sao Paulo state's third largest city, he added.
Some of the killings were perpetrated by criminals riding in vehicles, police said.
The daily O Estado de Sao Paulo, meanwhile, said the killings occurred hours after an off-duty policeman was killed during a robbery attempt at a gas station in the area.
No arrests have been reported so far.
Last July, a survey on violence published by the Latin American Studies Center said one million people were killed in Brazil between 1980 and 2011, making it the world's seventh most violent nation.