Hoops supporters were involved in running street battles with locals on Saturday, resulting in at least one supporter being admitted to hospital with head injuries.
Police confirmed visiting fans were among those held.
The Parkhead club were in the north east for a so-called ‘friendly’ match to celebrate 20 years since the opening of Sunderland FC’s Stadium of Light.
However, even before kick-off, social media became awash with images of fans in green and white Hoops brawling with locals and police officers in the town centre.
One local news agency reported Celtic fans being attacked near the stadium by a coachload of hooligans, singing ‘God Save The Queen’.
In one piece of footage, a flare appears to have been thrown into a shop where former English Defence League leader Tommy Robinson was conducting a book signing, dressed in a Rangers top.
In the incident which followed, in the Hendon area, a man was felled by someone brandishing a weapon before collapsing on the ground.
A spokesman for the North East Ambulance Service said:”We received a call from Police around 1.57 this afternoon.
“We treated one male with a head injury. His condition appeared to be serious at first. Our ambulance was on the scene within six minutes of the Police call.”
The victim was first taken to Sunderland Royal Hospital but after doctors concluded his injuries were not life-threatening, he was transferred to another hospital.
On Saturday night, Northumbria Police were forced to use their Facebook page to deny rumours that someone had died.
The statement said:” There are currently rumours spreading that there is wide scale disorder in and around our city centres and that there has been a fatality, this is not true.”
A local news agency reported that Celtic fans fell victim to an organised attack by local hooligans, who arrived by the coach load, singing “God Save The Queen”.
Police in riot gear were forced to intervene as fighting broke out in North Bridge Street in the city.
Police dogs and horses were used by officers who lined the streets in an attempt to separate fans before the game.
One onlooker said: “All the bars around the Stadium of Light were full of Celtic fans singing and having a nice time.
“At about two o’clock a white coach pulled up and off got a lot of soccer thugs, they did not have any identifiable colours of football teams.
“They were singing anti IRA chants and ‘God Save The Queen’.
Celtic fans used the website ‘kerrydale street’ to condemn the sale of alcohol inside the stadium, which they feel helped fuel trouble.
Assistant Chief Constable Helen McMillan, of Northumbria Police, said:“Unfortunately we did have some incidents of disorder in and around Sunderland between Sunderland and Celtic fans and while police dealt with them quickly, it is a shame these types of incidents happen at all.”
Last Friday, Celtic were fined £20,500 by football governing body Uefa after paramilitary flags were flown at a European tie at Celtic Park.
Celtic declined to comment.