The violence occurred after Newcastle were beaten 3-0 by Paolo di Canio's Sunderland at St James' Park.
Newcastle fans threw bottles and other missiles at police in the city centre, and the Metro had to be closed for a short period.
Police said they received reports of minor incidents, including the release of smoke canisters, before and during the match.
Chief Superintendent Steve Neill, of Northumbria Police, said: "The vast majority of fans were well behaved today and enjoyed the Tyne-Wear derby for the great occasion that it is.
"Disappointingly, there was some disorder involving what appear to be Newcastle United supporters following the match in the city centre, including an incident at Central Station.
"Disruptive behaviour of any kind is not tolerated. Inquiries will take place into these incidents and action will be taken against all those involved.
"This was very much a partnership operation and a lot of planning went into what is a large scale policing operation to ensure that genuine fans were able to enjoy the game.
"Public safety is always our number one priority during any football match.
"For those who chose to get involved in disruptive behaviour they were either dealt with swiftly by officers or will be subject to retrospective action at a later date."
The violence came just 24 hours after Millwall fans were involved in disturbances at Wembley.