According to the Health Ministry, of the 24 injured, 19 had sustained gunshot wounds, TASS News Agency reported.
The Ministry added that 25 medical teams were currently working at the site.
According to the Russian Investigative Committee, the student opened fire earlier in the day at the university premises.
The shooter has been detained and authorities have established his identity but were yet to make it public.
The Committee added that the suspect sustained injuries as he tried to resist while being apprehended.
Meanwhile, President Vladimir Putin has instructed Prime Minister (Mikhail) Mishustin to send Minister of Health Mikhail Murashko and Minister of Science and Higher Education Valery Falkov to the scene.
"The President conveys deep condolences to those who lost their relatives and friends as a result of this tragedy," a Kremlin spokesman said.
A law enforcement agency source told TASS that during the shooting some students locked themselves in universities auditoriums to hide from the attacker, while others jumped out of the windows.
The source added that the perpetrator was armed with 'traumatic' non-lethal weapon.
Videos circulating on social media shows students throwing belongings out of windows from buildings on campus before jumping to flee the shooter, the BBC reported.
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 as he went to class.
The Perm State University, one of the oldest in the Urals, is located around 1,300 km east of the capital, Moscow.
Earlier this year, a 19-year-old gunman opened fire in his old school in the central Russian city of Kazan, killing nine people.