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 (137 miles) 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.
"During a fire in the Oksochi psychiatric hospital 37 people died," regional investigators said in a statement, adding that 30 bodies had already been pulled from the wreckage.
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.
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.
The fire in Luka, which broke out in the middle of the night, reduced the decrepit wooden building on the outskirts of a village beside a forest to smouldering wreckage.
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.
Local authorities said the hospital housed patients with grave psychological disorders, making evacuation even more complicated.
Lydia Vasilyeva, 40, who lives near the hospital, said the fire spread very quickly.
"Many of the patients were pushed out of the windows. Many didn't want to come out or didn't come out immediately. It was very scary," she told AFP.
She said it was difficult to pinpoint the cause of the blaze but suggested a patient might have started the fire.
"In the summer they brought a patient here who they say was suffering from pyromania," she told AFP.
Another local resident said she was woken up by her cats and the sound outside.
"I looked out of the window and there was fire everywhere, the slates were cracking. I was crying, I was in shock," said Diana Akakiyeva. "It's lucky that it wasn't windy, otherwise everything would have gone up in flames."
Investigators said they had opened a criminal probe into suspected negligence causing death.
"According to preliminary information, one of the patients set fire to himself and his bed," the Investigative Committee said in a statement.
Investigative Committee head Alexander Bastrykin personally went to inspect the scene of the disaster.
Prime Minister Dmitry Medvedev also instructed the labour and social development minister Maxim Topilin to travel to the village.
Officials said concerns had already been raised about the state of the building and the administration had been told by the authorities to remedy violations in fire safety by August 1.
The Kremlin's human rights envoy, Vladimir Lukin, sounded the alarm over the state of psychiatric hospitals in the country, calling for a joint effort to improve oversight.
"The entire society, the people should protect citizens who have found themselves in a unique, difficult situation when they cannot protect themselves," Lukin said on radio station Moscow Echo.
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.
In 2009, 156 were killed in a nightclub fire in the city of Perm, 1,200 kilometres (700 miles) east of Moscow in one of the deadliest accidents in Russia's modern history.