Doria says the dead included two teachers and six students, and several more people had been hospitalized after sustaining injuries.
He said it was not yet known whether the two assailants were former pupils at the school.
Monteiro's mother, Tatiana Taucci, offered a possible answer, telling Band News while hiding her face from the camera that her son had been bullied at the school.
By Wednesday afternoon, Facebook had taken down Monteiro's page.
Marcelo Salles, commander of police forces in Sao Paulo state, said: "It was an unspeakably brutal crime". The suspects are believed to be two teenagers, who shot themselves after the rampage.More news: All 157 aboard, including 8 Americans, killed in plane crash over Ethiopia
Governor Joao Doria said the two attackers were believed to be between 20 and 25 years old, adding that authorities do not believe they were former students.
The attack took place at around 9:30am during a recreation period for some students, authorities said.
Crime scene photographs released by police show Monteiro, his head lying in a pool of blood, dressed in black with a machete tucked in his trousers.
"My friend was stabbed in the shoulder and my other friend was shot", she said.
Horacio Pereira Nunes, a retiree whose house is next to the school, said he began hearing shots around 10 a.m. "I thought [the sound] was from bombs", said teacher Sandra Perez.More news: Emerson concerned Hazard will leave Chelsea
School shootings are rare in Brazil, even though the country is one of the world's most violent, with more annual homicides than any other.
Far-right President Jair Bolsonaro made relaxing gun control a cornerstone of his campaign past year. Soon after his January 1 inauguration, Bolsonaro issued a decree making it easier to buy a gun.
"A monstrosity and cowardness without equal", Bolsonaro wrote in a tweet expressing his sympathies for the families of the victims of Wednesday's attacks.More news: Google Releases Android Q Beta for Developers, Early Adopters