Lt Col Marcelo Granja of the Goiania police department tells reporters the shooting occurred Friday at Colegio Goyases, a private school.
The teen was taken into custody.
Granja says the shooter is the son of a police officer who used his father's .40 caliber pistol.
A student who escaped the shooting unhurt tells the G1 news portal that the suspect was bullied and called "stinky" because he never used deodorant.