Hill said by administering three vaccines to the boy in error, the nurse failed to provide services to the boy with reasonable care and skill.
The family said in the report they hoped this complaint would act as a prompt for other children and families to not receive this type of care in the future.
"It was probably an honest mistake — but had a major impact on our family …."
The nurse told the boy's father of the error immediately but waited until the following day to tell a doctor.
Hill said it was also "critical" that the nurse didn't advise a doctor of the adverse event until the following day.
"The medical centre had not taken reasonably practicable steps to prevent the nurse's error. Accordingly, it was found vicariously liable for that error."
The medical centre, of whom the nurse was employed by, was also told to apologise to the family and provide the Health and Disability Commission with an audit of vaccination-related documents.
If the audit did not reflect full compliance, further action would to ensure standards were being meet would need to be taken, Hill said.
Another HDC decision revealed an obstetrician who failed to recommend a Caesarean section to a woman carrying a baby with an abnormal heart was also told to apologise to the mum.
After proceeding with an induction, an emergency C-section was done and the baby was delivered in a poor condition, with no heat beat and no respiratory effort.
Immediate resuscitation was carried out, the baby survived but suffered brain injury.
Deputy Health and Disability Commissioner Rose Wall said the obstetrician failed to provide services to the woman with reasonable care and skill.