A three-year-old child has been seriously injured after allegedly being left in a burning car stolen by her father.

The girl was pulled from the flames by police after the vehicle crashed into a barrier on the Great Eastern Highway in Perth's outer north-east suburbs.

She was taken by ambulance to Princess Margaret Hospital where she is in a serious but stable condition.

A 25-year-old man from East Victoria Park has appeared at a bedside hearing in Royal Perth Hospital charged with multiple offences, including aggravated assault occasioning bodily harm, being armed in a way that could cause fear, stealing a motor vehicle and driving with a blood alcohol level in excess of 0.08 per cent.

He was remanded in custody.

The incident unfolded when police were called to a house in Ellenbrook shortly after 10:00pm (AWST) on Sunday night after receiving reports of a serious assault and a man damaging the property.

Before officers arrived the man allegedly stole a car and left the scene, taking his young daughter.

Police had concerns for the child's safety due to her father's behaviour and fears he may have been driving while intoxicated.

Police did not give chase 'because of fears for child's safety'

The vehicle was spotted being driven with the headlights turned off on Lloyd Street in Midland about 11:00pm.

Officers said they attempted to stop the car, but the driver refused to pull over.

"Due to the fact there was a child in the vehicle, officers did not engage in a pursuit, but attempted to monitor the movements of the vehicle," a police spokesman said.

Soon after, the car was found crashed and in flames near the intersection of the Great Eastern Highway with Roe Highway.

The child was still inside the burning car, and the man had left the scene.

Midland police officers pulled the child from the wreckage and she was taken to hospital.

It is also believed the car crashed into a Toyota Yaris on the Great Eastern Highway before hitting the barrier.

Police later found the man on Beaconsfield Avenue in Midvale.

He was arrested and taken to Swan District Hospital.

Acting Superintendent Steve Byrne said the actions of the police officers had saved the child's life.

"I think there's no question about that, the child was in quite a serious condition," he said.

"Although the fire was contained to the engine, if it wasn't put out it could have spread quite easily to the rest of the vehicle."

He said the girl had suffered severe internal bleeding and had undergone emergency surgery and was now in a spinal splint.

The father's actions were "unfathomable", he added.

"The violence inflicted on the family by this gentleman is unfathomable, but to leave a child like that to flee for your own concern, I guess, and not have any concern for your own child, I just can't imagine somebody doing that," he said.