The tragic death of the young girl has been referred to the ACT coroner who will determine whether an inquest is needed.

The child was taken to the hospital on July 4 when a number of tests were carried out. It is understood a decision was made to transport the girl to Sydney but she died before this could happen.

The family of the five year old issued a statement, saying they were not told what was happening until it was too late.

"We lost our daughter at Canberra Hospital. No one helped her until it was too late. No one told us what was happening before it was too late," the family said.

"No one explained to us how she died. My family has no answers and we are broken. This was an entirely avoidable incident with consequences that will now last a lifetime."

Health Minister Rachel Stephen-Smith said she had received a briefing on the death, as had Deputy Chief Minister Yvette Berry, who was acting health minister at that point.

"The death of any child is a tragedy and our thoughts are with the family at this really, really difficult time," Ms Stephen-Smith said.

"I also want to assure people that the staff who were involved in this are receiving support and the hospital is very conscious that those staff receive the debriefing and support that they require."

"I can't speak to any of the details of it because of the privacy considerations but also the investigations that are underway."

Opposition health spokeswoman Leanne Castley met the family and said it was horrific.

"We met with the family [on Tuesday] and spent a couple of hours hearing about this story," she said.

"This family is heartbroken. This is truly tragic.

"There is a family completely devastated and their little five-year-old girl is not at home."

A Canberra Health Services spokesman said its thoughts were with the family at this difficult time. He confirmed the death had been referred to the coroner and said the service could not comment further.