The 29-year-old woman, who was not identified, pleaded guilty last week and was sentenced to six months' supervision.
A drug search at the woman's house resulted in the discovery, and her partner was also arrested on drug charges.
Acting Senior Sergeant Andrew McDonald told BBC News that the woman's actions amounted to child abuse.
He stated: "Child abuse is family violence in these circumstances, and it is clear this baby and its mother needed help.
"People often believe drug-related activities are victimless, but it affects the people around them."
Warren Brookbanks, a professor of law at the University of Auckland, said it would have been difficult prove that the woman had deliberately administered cannabis to her baby if she hadn't pleaded guilty.
He explained: "It would be necessary for the prosecution to prove that the mother both knew she had cannabis in her system, and that she intended to administer it to the baby."
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