Earlier it was reported that 15 people have been killed but the death toll has since risen.
"They were migrant workers. We are trying to confirm which (ex-Soviet) republic they came from," an emergencies ministry spokesman said.
Unconfirmed news reports said the migrants came from the impoverished Central Asian nation of Tajikistan.
It is common for Moscow markets to employ cheap labourers from the region without giving them proper housing conditions.
The blaze broke out in the early hours of Tuesday at a market on the southern outskirts of the city called Kachalovsky. Read More