It was not immediately clear what triggered the blaze.
The fire was the latest tragedy to hit a psychiatric institution in Russia, where outdated Soviet-era infrastructure is still in widespread use and managers often take a lax approach to fire safety.
Scores of people also die in house fires each year.
A fire at a psychiatric hospital in northwest Russia in September 2013 left 37 people dead while another blaze in April of the same year killed 38.
In 2009, 156 people were killed in a nightclub fire in the city of Perm, 1,200 kilometres east of Moscow in one of the deadliest accidents in Russia's modern history.