The committee later said that 28 people were being treated after the attack.
The gunman was detained, Russia's Interior Ministry and a university spokesman said. Initially, authorities said that the gunman had been killed after the shooting, but later reported that he had been wounded and taken to a hospital.
Students and staff locked themselves in the rooms, and the university urged those who could leave campus to do so. Some were seeing jumping out the window.
The perpetrator, who was an 18-year-old student at the university, used a "traumatic" firearm, according to the Perm State University press service. Such guns are designed to fire non-lethal rubber or plastic projectiles, but can be modified to fire other ammunition.
The student had earlier posted a social media photo of himself posing with a rifle, helmet and ammunition.
Shooting incident at Russian university – DW's Juri Rescheto reports
"I've thought about this for a long time, it's been years and I realized the time had come to do what I dreamt of," he said on a social media account attributed to him that was later taken down.
He indicated his actions had nothing to do with politics or religion but were motivated by hatred.
Talking to DW Russian, reporter Alexei Trapeznikov said the suspect used "very large caliber ammunition."
"I walked down the hallway, I saw a dead body, a woman is screaming," said Trapeznikov, who works for Rossiyskaya Gazeta from Perm.
"It was an unreal, nightmare image."
It wasn't immediately clear how many victims sustained injuries from the shooting or from trying to escape the building. Earlier media footage from the scene showed students jumping from first-floor windows to escape the building, landing heavily on the ground before running to safety.
"Some of them have been hospitalized with injuries of varying severity," the Investigative Committee said in a statement.
"There were about 60 people in the classroom. We closed the door and barricaded it with chairs," student Semyon Karyakin told Reuters.
Russia's Investigate Committee has opened a murder probe into the aftermath of the incident. President Vladimir Putin had been notified of the shooting, the Kremlin said, adding that the health and science ministers had been ordered to travel to Perm to coordinate assistance for the victims.
"The president expresses sincere condolences to those who have lost family and loved ones as a result of this incident," Putin's spokesman Dmitry Peskov told reporters.
"This is a great loss not only for the families who lost their children but for the whole country," Putin said in televised remarks.
Second school shooting in six months
Regional authorities said that classes at local schools, colleges and universities were cancelled on Monday. The university, which has 12,000 students enrolled, said that about 3,000 people were on the campus at the time of the shooting.
Russia has strict restrictions on civilian firearm ownership, but some categories of guns are available for purchase for hunting and self defense. The country has relatively few school shootings due to normally tight security in educational institutions and gun ownership laws.
In May this year, a lone teenage gunman opened fire at a school in the city of Kazan, killing nine people and wounding several more. It was Russia's deadliest school shooting since 2018, when a student at a college in Crimea killed 20 people before killing himself.
Mourning in Kazan
Editors note: Earlier versions of this story stated a higher death toll and the death of the suspect. This was based on initial local reports which have since been altered. The previous versions of the article also wrongly placed the city of Perm in Siberia. The city is located in the Ural region of southwest Russia.