The market was designed by the same architect who drafted the plans for an aquatic part where a similar roof collapse killed 28 people two years ago, Echo Moscow radio station reported.
Russian media said preliminary investigations have suggested that collapse of the roof over the Baumansky market in the northeastern part of the capital was caused by recent snowfall.
Local media reports said up to 15 people may still be trapped inside the building, however a senior emergency situations ministry official said it was possible that dozens were still inside, according to the Interfax news agency.
The injured were rushed to hospital.
The market's architect, Nodar Kancheli, was placed under investigation last year in connection with the collapse of the roof over the Transvaal aquatic park on February 14, 2004, also following relatively heavy snowfall.
Echo Moscow said construction of the Baumansky market in Moscow was "not standard" and consisted of "a hanging shell of reinforced concrete" that was supported by a system of cables rather than with supports on the ground.
The report said the design of the market called for the structure to be checked regularly by the authorities.
The architect maintained that the incident at the Moscow Transvaal aquatic park was a terrorist attack, coming just after a bombing of a Moscow metro station which killed 41 people.
Wet snow had been falling in the Russian capital for several hours the previous night.