Moscow chief prosecutor Yury Syomin said the two admitted they committed the act "because there were many people of Asian origin" working at the market.
Five of those killed at the Cherkizovsky market are believed to be from China, and one from Vietnam.
Investigators are still identifying the others.
Terrorism and a dispute between criminals had been among the possible explanations being investigated by police.
(Interfax, ITAR-TASS, AFP)