Nine people were injured in the fire and 200 were evacuated from the building, which houses a hotel, the ministry said on the Telegram messaging platform.The fire was extinguished just before midnight (2100 GMT) and room-by-room inspection was carried out.
Russia's Investigative Committee said on Telegram they had opened a criminal case into the cause of the fire, which broke out on the fifth floor of the building.
The 41-year-old building in Moscow's Tagansky district houses the MKM hotel on the lower floors as well as apartments converted from a previous hostel on the upper floors, Russian agencies reported.
Russia's TASS agency reported, citing an unnamed emergency services official, that arson was the preliminary cause.