The 12-year-old from Rumney in Cardiff said he thought he was going to die when the incident happened as he played near his home.
South Wales Police is investigating the incident as a possible hate crime.
The Cardiff-born child who is of middle eastern descent was not physically hurt but was treated for a panic attack.
The boy, who said he had recently suffered racial abuse from other children, had been playing near his home when he went to retrieve a ball from a grassed area nearby.
"I went to get the ball and the children who hassle us were walking past and started saying things," he said.
"I told them to leave me alone but then a woman pulled up alongside them in a car.
"They said something to her and she said to me: 'I'm going to kill you and your mum and beat you up'."
He said he started to walk home but heard "a loud car noise, I think it was revving" and turned around to see "she had gone up on the pavement and was driving very fast right at me".
"She stopped about a metre from me but I thought she was going to kill me, I'm going to die.
"I could see her and the two women in the car with her laughing.
"I was crying, screaming, my legs wouldn't work. I was so scared and ran home.
"My mum phoned the police straight away but the woman had already gone."
He was taken to hospital later that night after suffering a panic attack.
The boy said in the last month he has been repeatedly told to "go home" and "you don't belong here" by some children.
He said: "Now I'm frightened to leave the house in case this woman does something again. I was born in Wales, this is my home, I'm British, but I don't want to be here anymore, I'm scared."
The boy's father - originally a refugee from Jordan - said the family have been left so scared by the alleged incident, they are considering leaving the country.
He said: "These children used to play with ours but something has changed recently. We have been told to be vigilant after recent terror attacks and I can't help but worry this change is linked to that.
"I have been in this country since 1993, but I have never had a problem as bad as this. I'm thinking maybe we should move from our house or leave the country.
"We have been happy here and have lovely neighbours but are just so scared this could happen again."
Supt Stephen Jones, from South Wales Police, said they "take any form of hate crime extremely seriously" and are looking for the car involved, which is possibly a Vauxhall Astra Convertible.
He added: "A supportive action plan has been triggered which means patrols in the area have been stepped up along with visits to the family home.
"Cardiff is a diverse city and its communities are made up of people from many different backgrounds. It is a tolerant city where cohesion thrives and any hostility or prejudice which targets individuals because of their ethnicity or religious beliefs will not be tolerated."
The family of a schoolboy who said he was threatened by a female driver who mounted the pavement and drove at him, say it had followed racial abuse.