Newcastle supporters are thought to have thrown missiles, including bottles, at police in the city centre.
The violence saw the city's Metro service closed for a short period of time.
Northumbria Police tweeted: "There have been pockets of disorder involving #NUFC in #Newcastle city centre, no major disruption, officers are on scene and dealing [with it].
"CCTV and evidence is being gathered and action will be taken against anyone involved in these sporadic incidents in #Newcastle #derby"
Sunderland won the match 3-0 against their local rivals to boost their hopes of Premier League survival.