Police confirmed the deaths and said "many" officers were at the scene to establish what happened.
It is understood the incident took place at a market outside the landmark Kaiser Wilhelm Memorial Church, with images on social media showing the damaged truck and debris.
Briton Emma Rushton, who was in the market, saw the lorry rush past her at speed and said it could not have been an accident.
She told Sky News she only missed being caught in the chaos because she had climbed up some steps to take a seat.
National Mackem Day 2022: 14 things you'll only understand if you're from Sunderland
Met Office announces yellow weather warning for thunderstorms across North East following heatwave
Durham police appeal for help to find 33-year-old in connection with alleged burglaries
Campaigners rally against Local Plan after farmland in Cleadon earmarked for 156 homes
Banned and uninsured Sunderland driver given jail warning by judge
Ms Rushton said: "The stall that we bought our mulled wine from was completely crushed. People were tearing off wooden panels to get out."
She added: "It was not an accident. It was going 40mph, it was in the middle of the market.
"There was no way that it could have come off the road and it showed no signs of slowing down."
Police later tweeted to urge people to stay at home and refrain from spreading rumours, adding that officers were working at full speed.
Julian King, European commissioner for the security union, tweeted: "My thoughts are with all those affected and their families in #Berlin tonight."