The shooter, reported to be a 18-year-old student, walked on to the campus on Monday morning and started shooting.
Students and teachers barricaded themselves inside the university building; others were seen jumping from windows.
The Perm State University press service said the perpetrator used a so-called “traumatic” firearm; such guns are designed to fire non-lethal rubber or plastic projectiles, but can be modified to fire other ammunition.
Russia’s Investigative Committee opened a murder probe in the aftermath of the incident.
The gunman had been detained, the Interior Ministry said, but a spokesperson from the university said he had been killed.
The regional heath ministry said there were injuries both from the shooting and from people trying to escape the building.
One of the university’s professors, Ivan Pechishchev, told the BBC he saw students running from a building, and people jumping out of the second floor windows as he went to class.
“They jumped out in some horror, screaming,” he said. “One of the students told me that it was a shooting. I heard pops, everyone began to scatter in different directions.”
Perm is about 700 miles east of Moscow, with a population of about 1 million. The university enrolls some 12,000 students.
In May, a gunman opened fire at a school in the city of Kazan, killing seven students and two teachers.