Video on social media, apparently taken minutes after the crash, showed dozens of people in Muslim dress, including children, screaming and rushing to see what happened.
The nearby Newcastle Central Mosque said the collision happened just as people were leaving Eid prayers.
"This woman, an African woman, came driving and just drove all over people," a witness told the Chronicle.
"The car was going on and people tried to stop the car. There were many injured people, two seriously."
Another witness, Asif Anwar, said: "The lady lost control of the car and hit some people. Two of them were kids.
Newcastle MP Chi Onwurah, who said on Twitter that she was one of thousands celebrating Eid in the city, tweeted: "I was at the prayers earlier and there was so much joy and unity. Thinking of those affected by what I am told was terrible accident."
Britain is on high alert for terror-related attacks involving vehicles after a string of them.
A man drove a van into Muslim worshippers leaving two London mosques on June 19, killing one and injuring others. Police said that was a terror attack directed at Muslims.
Police in Newcastle have put extra officers on patrol to reassure people.
