"Seven people have been killed and three injured, two of them are women, they are all Tajik nationals, who lived and worked on the garage site," Igor Kuryakov said.
A total of 20 Tajik workers were rescued by firefighters. The fire in the underground car park, which was under construction, has been put out.
The emergencies ministry said that the area, where the fire started and quickly spread across 150 square meters (1,614 square feet), was used by the migrant workers as a make-shift living space.
A police source said fire and safety regulations had been broken in the make-shift dormitory where some 100 people lived.
"Around 20 home-made rooms had been built for workers to live in," a police source said. "All of them were lined with flammable materials and heated by electric heaters."
Fire investigators are currently working at the scene.
The fatal fire is the second in the past month. On December 28 three people were killed and three injured in a blaze that broke out in a workers' dormitory in Moscow.