Two children could be seen leaping from the third floor of the four-storey School Number 175 as gunshots sounded, in a video filmed by an onlooker that was circulated by RIA.
Some Russian news agencies reporting two teenage gunmen were involved and others said a sole shooter took part.
RIA said one 19-year-old gunman had been detained and that an explosion had been heard at the school. Footage posted on social media showed a young man being pinned to the ground outside the school building by a police officer.
Footage also showed emergency service vehicles parked outside the school, with people running towards the building.
It was not clear whether any other shooters remained at large. Nor was it immediately clear what the motive for the attack was.
School shootings are rare in Russia. One of the last major shootings of its kind took place in Russian-annexed Crimea in 2018 when a student at a college killed 19 before turning his gun on himself.
Kazan is the capital of the Muslim-majority region of Tatarstan and located around 450 miles (725 km) east of Moscow.
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The Beslan (Russia) school siege started on 1 September 2004, lasted three days, involved the imprisonment of more than 1,100 people as hostages and ended with the deaths of either 331 or 334 people, over half of whom were children. Initiated by armed Chechen separatists. It is thought to be the deadliest school shooting in modern history.