The bodies of 12 people, two of them women, were found in the residential building in the mainly Muslim Bashkortostan region, the regional Investigative Committee, which probes serious crimes, said in a statement.
"They are believed all to be members of a social rehabilitation centre. Their identities are being established," investigators said.
Residents said the single-story building in the town of Sterlitamak, about 1,200 kilometres east of Moscow, housed a private drug rehabilitation centre, ProUfu.Ru regional news website reported.
The bodies had "no visible injuries", investigators said.
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"Based on the appearance of the bodies, they died from carbon monoxide poisoning," the head of the emergency service in Bashkortostan, Marat Latypov, told Interfax news agency.
The head of the Bashkortostan region, Rustem Khamitov, said the victims were undergoing work therapy to get rid of "harmful habits".
He called for an investigation into why the "12 people were living in a small room with barred windows and a metal door."
The fire was reported at 3:00 AM Moscow time and took almost two hours to extinguish, the regional emergency situations ministry said.
In 2013, 37 people were killed when a fire swept through a psychiatric hospital in northwestern Russia.
Russia is gripped by drug addiction fuelled by easy access to narcotics with the head of the federal anti-narcotics service estimating last week that 7.3 million people were addicted to drugs.