The blaze broke out Tuesday morning, Moscow time, in a ramshackle three-story building near the Kropotkinskaya metro station, The Moscow Times reported.
Firefighters managed to save 20 residents.
Five of them, including two children, were hospitalized for burns and smoke inhalation, the Emergency Situations Ministry said. ITAR-Tass Wednesday said authorities had opened a criminal case in the investigation of the fire.
The building housed nationals of Russia, Tajikistan and Kyrgyzstan.
A city hall source said the building has been scheduled for demolition since 2003.
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