The man was believed to have been killed by a native of the North Caucasus, a region in southern Russia where the people are predominantly Muslim. Caucasus natives work in the shopping center and at many vegetable markets around the Russian capital.
The Investigative Committee, Russia's main investigative agency, said in a statement that the 25-year-old man was killed in a dispute over his girlfriend as the couple returned home on Thursday. Investigators have questioned witnesses, the statement said.
Police released a photograph of the suspect taken by a security camera, but he has not been identified.
Video streamed live on Dozhd television showed the unrest in Biryulyovo, a working-class district in far southern Moscow. Hundreds of ethnic Russians were involved in the protests, and some of them chanted nationalist slogans.
The city police department called up additional forces to try to quell the violence.
Police stepped up patrols throughout the city and moved to close off a square just outside the Kremlin to prevent a repeat of 2010 riots, when thousands of nationalists and soccer fans protested the killing of an ethnic Russian during a fight between soccer fans and natives of the North Caucasus.
Riot police detained several people after demonstrators shattered windows at the shopping center. Other demonstrators then threw bottles and trash at the officers to demand the release of those detained, the Interfax news agency reported, citing police.
Hundreds of people set off from there for the vegetable warehouse, marching through the streets. Moscow police chief Anatoly Yakunin said during a televised briefing that the demonstrators overturned cars.
Helmeted riot police blocked their path, but dozens still managed to break into the warehouse. Police said they detained about 200 people at the warehouse. Later in the evening, demonstrators again gathered outside the shopping center and clashed with police, who said about 100 more were detained.