Authorities believe Andrey Emeliannikov killed his health and safety teacher Sergey Danilov after he confronted him over truancy.
The teenager allegedly posted photos of the killing online, in which he can be seen standing over the 44-year-old's body holding a knife, according to Russian news agency TASS.
The bodies of Mr Emeliannikov and Mr Danilov were discovered in the classroom by another teacher, according to local media.
Mr Danilov, described as a "kind and responsive" teacher, had been Mr Emeliannikov's head of class and was reportedly responsible for his overall academic performance.
Students and teachers at the school expressed their shock at the horrifying incident.
One teacher told local media: "Intellectually, [Mr Emeliannikov] was always a little ahead of the others."
One of Mr Emeliannikov's fellow students described him as a "well-read, self-possessed and kind person".
Authorities told TASS a video found on the suspect's phone could serve as evidence in the ongoing investigation.