The teenager has also been charged with assault with intent to rob and aggravated wounding and has been remanded in Oranga Tamariki's care until July 16.
Because of his age, his name is permanently suppressed.
Detective Senior Sergeant Lloyd Schmid said a dedicated team had worked on the investigation and were pleased to get a swift result.
"Police appreciate the Grey Lynn community has been very concerned about the attack and we hope by apprehending these offenders that this will offer some reassurance to both of the victims, their family and the community," Schmid said.
"This has been a traumatic ordeal for the victims and there has been a tremendous amount of support offered by the community which has been greatly appreciated.
"This was very distressing for the family, who suddenly found their mother and son seriously injured, and police would like to thank the community for the support they have offered."
Gita Patel owns Hylite Dairy with her husband Navin and son.
Navin Patel said the couple had owned the dairy for 15 years and never had any trouble.
He was visiting family in Canada when his wife and son were injured and immediately flew home.
"I think it's just a one-off. I have been here 15 years and nothing like this has happened," he told the Herald.