According to Russian media reports, the collapse was due to domestic gas explosion.
Tass news agency quoted Deputy Director of the National Guard in the region, Nikolay Merzlyakov, as saying that the bodies of four people have been recovered from under the rubble.
The rescue operation was underway as more people could to be trapped under the rubble.
Four people were also injured in the incident.
More than 30 apartments have been affected by the collapse, said an official.