Alexander Chupriyan, a deputy emergency situations minister, said the victims, all of them women, found themselves trapped in the five-story building, with the escape routes blocked with metal grilles, and they died as a result of inhaling fumes before firefighters arrived at the scene.
"They could not leave the premises without outside help, as only one emergency exit was open," he said.
The ministry said it had asked a court earlier this year to close down the hospital over fire safety violations, but that the court rejected the request.
A criminal investigation is now under way to establish the cause of the fire, with arson being considered as the main theory.
"There is a 90% probability it was arson," Yury Nenashev, head of the emergencies ministry's fire safety directorate, said.