The Home Ministry said the gunman has been taken into custody.
The Perm State University Press Service said that the perpetrator used a firearm designed to fire non-lethal rubber or plastic bullets, but that could be altered to fire other cartridges.
University students and staff locked themselves in rooms and the university urged those who were in a position to leave the campus. The official Tas news agency, citing an unnamed source, said some students jumped out of the windows of a building.
The exact number of injured is not yet known and their number could be between six and 14. It is not clear if any of them were injured after jumping off the building.
The city of Perm, located about 1,100 km east of Moscow, has a population of about one million and about 12,000 students at the university.
It was not immediately known what the gunman’s motive was behind the attack.
In May, a gunman opened fire on a school in the city of Kazan, killing seven students and two teachers.