The Health Ministry of the Perm region reported 14 people wounded. The different numbers couldn't be immediately reconciled.
The assailant entered the Perm State University campus Monday morning "with an offensive weapon" and opened fire, the university said in a message on its Telegram channel that warned students to "please be careful."
Students and staff of the university locked themselves in rooms, and the university urged those who could leave the campus to do so.
The gunman was later detained, Russia's Interior Ministry said. The Investigative Committee has opened a murder probe in the aftermath of the incident.
The suspect in the shooting is a male student and has been identified, the state investigative committee said. It was not immediately clear if he is a student at the university. The suspect resisted law enforcement officers during his arrest and was wounded, said the committee.
The state Tass news agency cited an unnamed source in the law enforcement as saying that some students jumped out of the windows of a building. The regional heath ministry among those wounded were injuries both from the shooting and from trying to escape the building.