The fight broke out at about 8 p.m. Friday after members of the Moscow Shield organization "checked the immigration status of citizens from the near abroad" at a Moscow address, a police spokesman said Saturday.
Video footage of the event shows Moscow Shield members, who were wearing masks and holding air pistols, entering the address and then bringing out a group of young men, who appear to be from Central Asia, back outside, RIA Novosti reported.
It was unclear who else was involved in the fight, but police said about 60 people were arrested, including 25 Moscow Shield members.
It was not reported how many people participated in the brawl.
All of those who were arrested were later released, and two were fined for migration offenses, police said.
Moscow Shield is known for carrying out searches for illegal immigrants before contacting authorities.