"Out of the 10 wounded people, two have died," police spokeswoman Sofya Khotina told Interfax news agency. "Fifty people who took part were arrested."
Reports said the fight at the Khovanskoye cemetery involved 200 immigrants from former Soviet Central Asia and residents from Russia's volatile North Caucasus.
The interior ministry said the fight involved firearms and appeared to have been sparked by a dispute over who had the right to work on the cemetery, a massive 200-hectare site on Moscow's southwestern rim.