The student, a 10th-grader, was disarmed and taken into custody.
Investigative Committee spokesman Vladimir Markin described the suspect as an excellent student who may have had an emotional breakdown.
He said the suspect will undergo a psychiatric evaluation.
Investigators said the student entered the school on February 3 armed with two guns, fatally shot the teacher, and opened fire on police who responded to the emergency, killing one and seriously injuring a second.
Reports said the student was taken into custody after negotiations involving his father.
No injuries were reported to other students at School 263.
Russia's interior minister, Vladimir Kolokoltsev, and other senior officials had rushed to the scene of the incident.