Health Ministry spokesman Oleg Salagay told RIA Novosti preliminary reports indicated two of the dead were medical personnel.
"Three people survived -- a medical nurse led two patients out of the burning building," Salagay said.
The Health Ministry spokesman said investigators believe 41 people were in the one-story building when the fire broke out at about 2 a.m.
Citing a police source RIA Novosti said most of the victims were probably sedated with prescription medications and died in their sleep of smoke inhalation.
The cause of the fire was under investigation and a criminal inquiry was under way, the report said.
The nearest fire station is 30 miles from the clinic and first responders did not arrive at the scene until about an hour after they were called, RIA Novosti said.