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The boy, who cannot be named because of his age, appeared in the Waitakere Youth Court this afternoon and entered no plea to a charge of murdering father-of-two Arun Kumar.
Judge Lisa Tremewan said the boy would next appear in the High Court at Auckland later this month. He will remain in custody until then.
He did not enter a plea on the other charge he faces - of robbing Mr Kumar with intent to assault him.
A 12-year-old boy, who also appeared today, entered no plea to the joint charge of robbery with intent to assault.
The 12-year-old will next appear in the Waitakere Youth Court next week. He will also remain in custody.
The boys' lawyers each applied for bail, which the Crown opposed.
Youth Court sittings are closed to the public but a large contingent of the boys' families was allowed in to watch as the two boys, both wearing dark shirts, stood side-by-side in the dock.
As he was led into custody, the 13-year-old mouthed "love you'' to his family members. Some of them yelled the same back at him from the public gallery, as well as comments like "be strong baby''.
Mr Kumar, 57, was stabbed in the neck in front of his wife during what is believed to have been an attempted robbery of the Railside Dairy in Henderson about 7.30am yesterday.
Police have said Mr Kumar's wife was unhurt but was traumatised, and was being helped by Victim Support and a police ethnic liaison officer.
Family members and friends have paid tribute to Mr Kumar.
"He was a hardworking man, a great husband and a father. A man so kind and humble, he did not deserve this,'' said Shirlyn Prasad Kumar, the daughter of Mr Kumar's cousin.
Friend Rohitesh Prasad said Mr Kumar's death was a "tragic end to a great guy''.