The all-day Hemlock Happening event had to be shut down early on the advice of officers because of the fight.
A number of police cars and riot vans were called to the festival at Bramcote Hills Park, Bramcote, at about 9.20pm on Saturday.
It is understood at least one person was arrested following the incident and nobody was injured.
Organisers say violence broke out “among groups of youths at various points around the periphery of the event” and the decision was made to call it off.
It meant the fireworks finale at 10.30pm was entirely cancelled.
In a statement, the organisers said: “This is the first time in 14 years that Hemlock Happening has had to be terminated prematurely and we are astonished and devastated that a tiny minority of our community should behave in the way that they did.
“Feedback meetings will follow after which the future of the event will be considered.”