Children as young as 10 were injured after a brawl broke out between more than 200 football fans in a coach park.
Five people were arrested in the wake of the fight after the Middlesbrough v Sheffield United game on Saturday.
Cleveland Police said youngsters were "terrified" by the violence, which left one police officer in hospital.
Sheffield United said the culprits were facing banning orders. Those held remain in custody while inquiries continue.
'Bring to justice'
Disorder began just before the final whistle when Blades fans thought their team scored a last minute equaliser, only for it to be disallowed.
Assistant Chief Constable Jason Harwin said the force would "absolutely not tolerate violence of this nature".
He added: "The vast majority of fans accept that football is a family game, watched by children, parents and grandparents.
"It's terrifying for children to witness such violence, or be innocently embroiled in it as their parents frantically try to keep them safe.
"Unfortunately a small minority of people behave in a manner which puts innocent fans at risk."
Sheffield United's chief operating officer, Andrew Birks, said: "We will not condone this type of behaviour, particularly when the vast majority of our thousands of our fans attend home and away fixtures simply to enjoy watching the Blades in action.
"We are assisting Cleveland Police and others to identify the troublemakers and bring them to justice, which may include the potential use of banning orders."
Middlesbrough won the Championship game 1-0.