Dozens of people were at the sports centre celebrating the Muslim festival of Eid, which marks the end of the fasting month of Ramadan, when the car left the road and drove up onto the pavement.
"The enquiries that we have made so far ... are telling us that this was not a purposeful act, it appears to be a tragic accident," said Darren Best, assistant chief constable for Northumbria police.
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He said three adults and three children had been injured; two of the children were in intensive care in hospital and one adult was on a high dependency unit. Police said a 42-year-old woman had been detained and was in custody.
"On Sunday June 25, at approximately 9:14 a.m., Northumbria Police received reports that a vehicle had collided with pedestrians outside of Westgate Sports Centre, Newcastle upon Tyne," the police said in a statement earlier.
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