The offences included assaulting emergency workers, affray, drug possession, possessing a firework or flare at a sporting event, being drunk and disorderly and failing to comply with a dispersal order.
A Cleveland Police spokesperson said: “A minority were intent on spoiling the day for everyone and pockets of disorder took place at the ground and across the town centre prior to, during and after the match.”
Sheffield Wednesday boss and chairman unhappy after attackers leave for Premier League
Why Sheffield Wednesday left Dennis Adeniran out completely against Charlton Athletic
Darren Moore dismisses Barry Bannan over-reliance notion after surprise Sheffield Wednesday sub call
Chris Wilder says Sheffield United "ready to rock and roll" after Middlesbrough draw
Charlton Athletic boss gives Sheffield Wednesday ‘favourites’ tag – admits Hillsborough frustrations
Tensions between both clubs were high heading into the fixture due to Middlesbrough’s compensation claim against Derby, which the pair reached a ‘resolution’ over on Friday.
Boro had launched legal proceedings against the Rams, claiming Derby's financial breaches cost them a play-off place in the 2018-19 season.
The match commander, head of specialist support & planning, superintendent Dave Sutherland, said: “The vast majority of fans from both clubs were simply there to have an enjoyable afternoon watching their team but sadly there was a small minority of people intent on taking part in disorder or criminality.”
Police also performed CPR to a man who suffered a ‘medical episode’.
It is understood he spent Saturday evening in hospital receiving treatment.
Police confirmed video footage obtained during the day will be analysed to identify and take action against anyone else suspected of being involved in disorder and criminality.
Chris Wilder’s play-off chasers won the game 4-1 to move up to sixth place and three points clear of Sheffield United, who have one game in hand over them.
New Bournemouth signing breaks foot
Kieffer Moore is set for a two-month spell on the sidelines after breaking his foot in Bournemouth's win over Birmingham on Wednesday.
The Welsh international striker only joined the Cherries – who currently occupy the second automatic promotion spot – from Cardiff City for an undisclosed fee on deadline day.
Bournemouth boss Scott Parker said: "Kieffer's a big disappointment.
"He going to be out for probably the next two months. It is disappointing.
"The luck on it. We brought him in, he came on for five minutes and landed on his foot, which is his opposite foot (to his recent ankle injury). It is a brand new injury and he's broken his foot."