The arrests include three men charged in connection with a serious assault of a man following the match.
Nine people have been arrested following disorder connected with the Scottish Cup quarter final match between Rangers and Celtic at Ibrox on Sunday.
There was mayhem at Ibrox on Sunday when fans from both teams invaded the pitch.
Sickening scenes saw flares fired into the midst of fans, while supporters, police officers and those working at the stadium came under attack.
A steward was seen being carried from the pitch, believed to have been injured in the chaos, and a number of people were pictured receiving medical treatment.
Celtic striker Tomáš Čvančara, who scored the winning penalty for his side, was interviewed for TV wearing a blood-stained shirt. He had been photographed intervening in an incident on field.
A member of Celtic’s coaching staff was also reportedly attacked.
There was also violence outside of the stadium following the game.
Three men, aged 54, 23 and 20, have been arrested and charged in connection with a serious assault of a man on Helen Street following the match. The men are due to appear at Glasgow Sheriff Court at a later date.
A number of officers and members of the public were injured during the scenes which took place on the pitch at the end of the match. Items, including pyrotechnics, were thrown and a 10-year-old child was struck by a coin.
A 54-year-old man was arrested and charged in connection with a police assault. He was released on an undertaking to appear at Glasgow Sheriff Court at a later date.
A 47-year-old man was arrested and charged in connection with an assault on a coach and player at the end of the match. He was also released to appear at a later date.
There were also other arrests in relation to a number of offences including abuse towards officers and culpable and reckless conduct. Vandalism and graffiti within the stadium are also being investigated.
Chief Superintendent Emma Croft, Greater Glasgow Divisional Commander said: “These were utterly disgraceful scenes and must be condemned by everyone involved in football and the wider society.
“No one should have to face such extreme levels of violence and hostility, and those responsible will be identified and face the consequences.
“Several officers and members of the public, including a child, were injured as a result of what unfolded. This is totally unacceptable and shameful behaviour.
“It begs the question, does someone need to be critically injured or worse before this behaviour is treated with the seriousness it deserves?
“Policing will play its role in addressing these issues but it requires collective action by a number of organisations with whom we are currently engaging.
“Crucially, however, I would also call out the need for individuals who see fit to behave in such a despicable manner to take personal accountability. No game of football should be overshadowed by the behaviours of a few.”
Police Scotland say a “robust” investigation is ongoing and the force is working with both clubs as well as the Scottish Football Association as enquiries continue.
Chief Superintendent Croft added: “A policing enquiry team has been established today to investigate all incidents pertaining to the quarter final fixture and I would appeal to any member of the public who has information which may assist those enquiries to contact Police Scotland as soon as possible.
“I want to give my assurance that our investigation will be very thorough, and further arrests will be made in due course. For those involved in this kind of disorder, the message is simple: it is not a question of if, but when we will identify and come looking for you.”
Anyone with information can call 101 or can contact Crimestoppers anonymously on 0800 555 111. Information can also be sent directly to the investigation team. The Major Incident Public Portal (MIPP) can be accessed here.