They had mobility issues and could not be quickly evacuated, the Russian news agency Interfax reported.
Four managed to escape the burning building in the village of Ishbuldino, Abzelilovsky district before firefighters arrived.
District authorities said that one of the survivors was a female staff member and three were residents who she managed to lead out of the one-story wooden building, Interfax reported.
The fire was reported to the emergency services at 12:53 a.m. Moscow time, and burned for more than three hours until the flames were extinguished at 4 a.m., Tass said.
Initial reports blamed "careless handling of fire" as the cause for the blaze that burned through the private care home, Tass reported. A further investigation is underway.