Some 400 angry demonstrators, mostly in their 20s or 30s, stormed into a vegetable store in a shopping center in the district of Biryulyovo in search of the migrant.
Police said, in all, about 1,000 people were involved in the riot.
Yegor Shcherbakov, 25, was fatally stabbed on Wednesday night by an alleged Caucasian or central Asian man, who fled the scene.
Local residents took to the streets on Saturday and Sunday, demanding justice and accusing authorities of covering up the crime and tolerating illegal immigration in the area.
The demonstration went violent on Sunday afternoon when a group of young men smashed windows in a shopping centre and set it on fire.
A YouTube video showed several men chanting nationalist slogans as they forced their way into the shopping centre.
Moscow out on high alert after the riots
After several people were detained, some aggressive demonstrators clashed with riot police and stormed the vegetable store where many migrants are employed.
Moscow Mayor Sergey Sobyanin ordered the setting up of an emergency response centre to handle the situation.
Police said that they had contained the riot and that five officers were injured during clashes with demonstrators.
Meanwhile, the city of Moscow was also put on high alert following the riot.