The fire broke out on the roof and spread rapidly throughout the hospital in the town of Ramensky, the ministry said.
"According to preliminary reports, 38 people were killed, including two medical staff," said health ministry spokesman Oleg Salagai, cited by the RIA Novosti news agency.
The emergency situations ministry said in a statement that 41 people were in the building at the time.
"Twelve bodies have been found" so far, it said.