Children as young as 10 have been injured as more than 200 football fans fought in a coach park, police said.
Officers arrested five people as fighting broke out following the Middlesbrough v Sheffield United game on Saturday, which left one officer in hospital.
Disorder began just before the final whistle when Blades fans thought their team had nabbed a last-minute equaliser, only for it to be disallowed.
Those arrested are currently in custody, with Cleveland Police saying they expect to make more arrests as the investigation continues.
Assistant Chief Constable Jason Harwin said: "We will absolutely not tolerate violence of this nature and we will work to identify the offenders and bring them to justice.
"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."
Middlesbrough won the Championship game 1-0 with a first-half goal from Rudy Gestede.