The incident happened outside Westgate Sports Centre in the west end of Newcastle shortly after 9am on Sunday morning.
Northumbria police do not believe the incident is terrorism related. The driver, a 42-year-old woman, was arrested at the scene and is in police custody.
Hundreds of people had gathered outside the sports centre for Eid prayers to mark the end of Ramadan, the Muslim holy month. Witnesses said prayers had ended but people were gathered in the car park afterwards.
Three children were among the injured, the ambulance service said.
A North East ambulance service spokesman said: “We received our first 999 call at 9.15 this morning to report a car that had mounted the kerb.
“We have taken six people to hospital, they have gone to the Royal Victoria infirmary in Newcastle, three children and three adults.”
Asif Anwar, 29, told the Newcastle Chronicle what he saw.
He said: “The lady lost control of the car and hit some people. Two of them were kids.”
The incident came six days after a man drove a van into a crowd of Muslims near Finsbury Park mosque in London, killing one. Anwar said his first thought was that it was a terror attack.
“It was chaos, everyone was panicking people just don’t know what is going on these days. Terrorism is what everyone was thinking straight away,” he told the Chronicle.
In a late morning update on Sunday Northumbria police said extra officers were on patrol among the community following the incident.
They reiterated there was nothing to suggest a terror link but that a full investigation was underway. No other suspects are being sought, the force said.
The event, called Eid in the Open, had been organised by Newcastle Central mosque. It began at 7.30am on Sunday morning, and was set to include food stalls and a bouncy castle.
In a statement on Facebook the mosque said: “Immediately after the Eid prayers when the people were starting to leave the venue, a car collided with pedestrians. The injured were immediately attended to by the emergency medical services and the police. All the injured have been taken to the hospital. We pray and hope that all those affected recover soon fully.
“We thank the emergency medical services, the police and over 100 volunteers from the mosque for their quick response to the incident. We were able to clear the area promptly ensuring there was no delay in the injured being attended to.
“We urge everyone to please pray for all those affected. The police are investigating the incident at the moment and we will give an update as soon as we have more information.”
Northumbria police said in a statement: “On Sunday June 25, at approx 9.14am Northumbria police received reports that a vehicle had collided with pedestrians outside of Westgate Sports Centre, Newcastle upon Tyne.
“Police inquiries are ongoing to establish exactly what happened but, at this time, it is not believed to be a terror incident.
“Emergency services are currently at the scene and six casualties have been confirmed.”