A 29-year-old man sustained facial injuries and lost several teeth during the disturbance.
Police say they received reports from local people of a fight taking place near Enniskillen Courthouse in East Bridge Street. Officers went to the scene and arrested four men and two women aged between 18 and 27. They were later released pending further enquiries.
Anyone who saw how the incident started is asked to contact police on 0845 600 8000, quoting reference number 62 04/10/12.