PHOENIX (REUTERS) - A six-year-old Phoenix girl received fatal injuries when her eight-year-old brother crashed the family car into a metal pole during a late-night drive in their pajamas, police said on Thursday.

The children were reported missing by their mother on Wednesday night, about the same time emergency dispatchers received a report of a moving vehicle with children inside, Phoenix police Sergeant Steve Martos said.

A patrol car spotted the 2010 Hyundai Elantra and followed it a short distance before the boy crashed the car into a pole about a block from the family's home, he said.

Officers aided the girl, but she died early on Thursday morning of her injuries, Mr Martos said, adding that she was not believed to be wearing a seat belt at the time of the crash and that a passenger-side air bag did not deploy.

Her brother had a minor ankle injury.

Mr Martos said the mother told police that she had bathed her children and put them to bed at about 9.30pm, only to find them missing some 30 minutes later. She also discovered the front door open and the car missing and initially feared that they had been kidnapped.

"This is just a horrific event," Mr Martos said. "The mom puts them to bed, tucks them in for the night and then wakes up this morning and finds that her six-year-old is dead. That's just a tragedy."

Investigators believe the children had driven about 8km and may have been on their way home at the time of the crash, he said.

The police did not identify the mother or children.