Police broke up the fight, which involved more than 60 people armed with metal rods, sticks and knives, and several participants were detained.
Members of both ethnic groups inhabit the town, which has a population of 10,000.
Meanwhile, police had to intervene to separate Ingush and North Ossetian youths who clashed today in a volatile border region between the two Russian regions.
Relations between Christian Ossetians and Muslim Ingush have been uneasy since a 10-day war in 1992 over the Prigorodny region. The fighting killed hundreds and forced at least 50,000 ethnic Ingush to flee.