Area Commander for Auckland East Inspector Jim Wilson said the person was "extremely remorseful" for what occurred.
He also said that police have wound down their presence in the area but we will continue to liaise with the school as inquiries continue.
Patrick Walsh, the headmaster of Sacred Heart College, confirmed that police had completed their investigation and that school will return as normal tomorrow.
In a message to the school community, he thanked them for their patience and quick response today.
The nature of the threat is still unclear but it was directed at two people connected to the school.
"The police have advised that, given the nature of the anonymous threat, we err on the side of caution and close the school for the day until their investigations are completed," Walsh's email read.
A college spokeswoman said boys had been asked to stay home or, if they had already arrived at school, to return home.