The fire was apparently started by a patient who was either smoking or deliberately set fire to his bed at the hospital in the village of Luka, 220 kilometres southeast of Saint Petersburg, officials said.
The single-storey wood-and-concrete building housed around 60 male patients including 15 who were bedbound, and the institution had been previously warned by the authorities to improve its fire safety.
Local residents told AFP that one of the patients was believed to suffer from pyromania.
A nurse perished in the fire that broke out at 2.45 am (2245 GMT) while saving patients. She left behind a husband and four children, locals said. Authorities were planning to decorate her posthumously.
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The blaze was the latest tragedy to hit a psychiatric institution in Russia.
In April, a fire ravaged a psychiatric hospital in the Moscow region, killing 38 people, most of them patients who were engulfed by flames as they slept behind barred windows.
Rescue teams were combing through the debris and taking away bodies in black plastic bags from the scene.
Novgorod region governor Sergei Mitin told AFP at the scene that 23 people had been rescued from the fire.
Ilya Denisov, a representative of the emergencies ministry, said it was still possible that more survivors could be found.
He said the firefighters were quick to react but that by the time they arrived the fire had consumed the entire building.