Two people reportedly opened fire and a 19-year-old man has been detained.
The attack happened some 820km (510 miles) east of Moscow.
An explosion was heard and reports said the second attacker was killed on the fourth floor of the building.
Kazan is in the mainly Muslim republic of Tatarstan.
Heavily armed police and emergency vehicles were seen outside school number 175 in Kazan. Footage shared on social media showed some children jumping from windows to escape as well as injured people being evacuated.
One video on social media captured a teenager lying on the ground apparently being detained outside the building.