"A man died in hospital from burns and another from complications due to chronic disease," said Margarita Istimenko, the press secretary of the health department in the Rostov Region.
A total of 43 people were in the two-story building in the town of Daraganovka, when the fire started early morning.
Istimenko said six victims of the fire were released from hospital Saturday.
"Two [psychiatric hospital] nurses, three inmates are still in a hospital in the town of Taganrog, three others are in a burns unit in [the regional center] Rostov-on-Don, and the other is in intensive care," she said.
The preliminary cause of the fire has been put down to negligence.
It was the latest in a string of fires that have hit medical institutions in Russia over the past few months. A fire in an old people's home took the lives of 63 people in a small town in the Krasnodar Territory, southern Russia in March. Breaches in fire prevention measures were officially declared the cause of the tragedy.
In December, a fire in a Moscow addiction clinic killed 46 people, and another 10 were killed in a fire in a psychiatric and neurological clinic in the Kemerovo Region in Russia's southwestern Siberia.