Korotangi Paki, 18, who is the son of King Tuheitia, pleaded guilty to two charges of burglary and one of theft from a car, relating to offences carried out in Gisborne in March, Radio New Zealand reported.
Paki's lawyer had pushed for a ban on media identifying him in the case, but later dropped the application. The teenager was granted bail and will be sentenced in July.
Tuheitia was not in court for his son's appearance but told Fairfax Media ahead of the hearing that the boy had gone "off the rails", culminating in the thieving spree with three co-accused after a drinking session.
But he said he decided to publicly rebuke his second-born child instead, forcing him to confront the embarrassment he had caused.
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"I think Korotangi has learnt his lesson," Tuheitia told Fairfax. "I think he knows what he has put me through now. I know he won't be doing anything else."
Tuheitia is descended from the first Maori king Potatau Te Wherowhero, who was appointed in 1858 by various North Island tribes which wanted a single figure to represent them in the way that Britain's Queen Victoria was felt to represent New Zealand's white settlers.
The current king worked as a truck driver before his coronation in 2006.
He refused to meet Prince William because his office felt the 90 minutes allotted for the face-to-face visit was insufficient, arguing he was "not a carnival act" for visiting dignitaries.