Videos posted to social media showed students dangling out of classroom windows before jumping to the ground below in a bid to escape.
Shootings are relatively rare in Russia. The country has strict laws on civilian gun ownership and requires people to pass psychological exams before obtaining a license for hunting and sport firearms.
In May, nine people died and 20 others were injured when a gunman opened fire at a school in the city of Kazan, prompting President Vladimir Putin to call for a tightening of gun laws.
Perm University is one of the oldest universities in Russia and is based 800 miles east of Moscow.
â Robyn Dixon contributed from Moscow.
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