Four people have also been taken to hospital.
A total of 110 people were registered as residents of the affected section of the building, regional authorities said.
Sixteen people including seven children have been evacuated.
The Emergency Ministry later said that 35 people are still missing, and it wasn't clear if they were in the building when it collapsed. But officials added that up to 40 people could still be trapped under the rubble.
National television broadcast footage of rescue workers combing through mangled heaps of concrete and metal in temperatures of minus 18 Celsius. Monday is a public holiday in Russian Federation.
Officials warned that two more sections of the Soviet-era high-rise on Karl Marx Street were in danger of collapsing.
In one sign of how serious the accident was, President Vladimir Putin was informed of the accident in the industrial city some 1,400km east of Moscow, according to the Kremlin.
The Soviet-era high-rise was built in 1973 and was home to around 1,100 people. Residents were evacuated to a nearby school.
The head of the Tajik diaspora in Magnitogorsk, Abulmajid Sharipov, told RFERL that a Tajik family of five was living in an apartment in the collapsed part of the building.
Billionaire Viktor Rashnikov, who controls the plant, called on city residents to help the victims.
The cause of the gas explosion is not immediately known.
Gas blasts have become a relatively common occurrence in Russian Federation over recent years as the country struggles to cope with aging Soviet-era infrastructure and loose safety requirements, according to Reuters.
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