The incident occurred late on Monday, when three attackers fired shots at four Turks at the Cherkizovsky outdoor market in northeast Moscow.
A large percentage of the workers at the Cherkizovsky market are from Russia's North Caucasus region and former Central Asian Soviet republics, as well as Vietnam and China. The market was the site of a bomb attack by far-right extremists in 2006, in which 11 people died.
Turkey's Embassy in Russia has not yet received any information on Monday night's attack from the Russian authorities, a spokesman said.
There have been a growing number of racially-motivated attacks in Russia in recent years.
On October 21, two assailants of Slavic appearance murdered a 37-year-old Uzbek, stabbing him in the back, chest and neck. Investigators ruled out robbery as a motive for the killing, as the attackers failed to take 10,000 rubles ($400) from the victim, who died at the scene. The killing also took place not far from the Cherkizovsky market.
Police and courts in Russia usually treat such cases as hooliganism, rather than racially- motivated crimes, leading human rights groups to express alarm over the increase in racist violence in the country.