According to the Interfax news agency, two gunmen opened fire in the school.
One of them – a 17-year-old – has already been apprehended.
Eight children and one teacher were reportedly shot dead, while two other children are believed to have died jumping out of windows to escape the shooters.
Local officials said some children were evacuated from the school but others still remained in the building.
Authorities said additional security measures have been put into place in all schools in Kazan.
The incident occurred as Russians returned to work and school following a 10-day national holiday to mark Labor Day and the 76th anniversary of Soviet Russia’s defeat of Nazi Germany in World War II.
Kazan, about 700 kilometres east of Moscow, is a city of 1.2 million people and is known as the “third capital of Russia”.
It is the capital of Russia’s Tatarstan region, which is mostly Muslim.
While school shootings are relatively rare in Russia, there have been several violent attacks on schools in recent years, mostly carried out by students.