The bill - backed by 400 members of the State Duma, with 226 votes required - will assign at least 20% of the retail space to Russian producers at clothing markets and 50% at food markets.
According to the bill, management companies handling market organization will be in charge of market operations.
The move comes after two local residents were killed and five others injured in a restaurant brawl with Chechens August 30 in northwestern Russia amid accusations that migrant criminal groups had bought off local police.
The incident sparked racially motivated violence in the community and a wave of nationalist protests elsewhere in the country against migrants from the Caucasus, who are a dominant presence at markets across Russia.