The children, suffering from cancers including leukemia, lymphoma, sarcoma and brain tumours and aged one to 15 years, had received between 9 and 17 per cent too much chemotherapy with the drug etoposide phosphate.
One of the children has since died, but state Health Minister John Hill insisted this was unrelated to the errors made at Adelaide's Women and Children's Hospital.
The treatment blunders, between 2005 and October this year, has been attributed to collapse of "corporate knowledge" in the Women's and Children's Hospital's oncology unit.
The problem was traced back to a computer program that was used to recalculate chemotherapy doses after the hospital switched from the more side-effect prone drug etoposide.
Following the departure of several senior hospital staff in late 2004, oncologists lifted the dosage without realising that the computer had already done this, giving the children "an unplanned additional amount of etoposide phosphate," it was stated.
The South Australian Government has now ordered an audit of all medical equipment in public and private hospitals used in cancer programs.
It was the second time this year the state Health minister had been confronted by a comprehensive failure in a cancer program, after the Royal Adelaide Hospital belatedly revealed in July that more than 800 patients had received inadequate doses of radiation therapy, Australian reported.
Mr Hill issued a public apology to the affected children and their families. "I am very sorry that this error has occurred, it is regrettable that mistakes were made," he said.
SA Health chief executive Tony Sherbon said expert advice from pediatric oncologist Marcus Vowels, who has already reported to the state Government, showed that "no harm was done".
Professor Vowels found, however, that the children were not adversely affected.
"My judgment, based on reviewing the patient records and my own experience with this drug ... is that no harm has been done," he said.
Dr Sherbon conceded that hospital checks had been inadequate, and needed to improve. Mr Hill said South Australia's Safety and Quality Council would review settings on all cancer equipment in the state's hospitals.
State Opposition health spokeswoman Vickie Chapman accused the Government of a cover-up because it was informed of the mistake on November 19 but only told the public yesterday.
"This (is a) case of having (an) extra dosage of chemotherapy treatment in children, for goodness sake," Ms Chapman said.
"These are the most vulnerable in our community and for the Government to conceal this is an absolute disgrace."
The Opposition has also questioned how the incorrect calibration of machines at the Royal Adelaide Hospital was not reported for two years.
Advocacy group Cancer Voices SA spokesman Ashleigh Moore said that while people made mistakes, the errors needed to be identified before they could interfere with the treatment.
He said people were questioning the quality of cancer treatment in Adelaide.