According to the New Zealand Herald report, the arrested minors were among the 716 children held in 2008-09 for offences ranging from unlawfully taking a bicycle and possession of cannabis to threatening to kill and assault with a weapon.
Superintendent Bill Harrison, national manager of police youth services, expressed shocked on learning about children who committed offences.
A four-year-old girl, two five-year-old girls and five five-year-old boys were among those arrested for dishonesty offences like shoplifting, burglary or theft valued under $500.
Police declined to give the details, citing privacy.
Stating the parents have a strong influence on children who commit crime, Ian Lambie, an associate professor, said that children generally model their action to that of their parents.
"High levels of aggression when very young are usually due to the family environment. If parents are violent, involved in alcohol or drug abuse or have psychiatric problems their children are more likely to act out," Lambie was quoted as saying.