"We are unable to provide specific details about ongoing investigations or cases. This is for the purposes of confidentiality, privacy and to ensure natural justice," the council said.
When contacted, the man declined to comment on "the accusations".
The Herald on Sunday then received a letter from his lawyer stating he had not been charged with any offence.
The Teaching Council said the safety of children and reputation of the profession were of paramount importance.
"There are steps available to us to ensure this. We can ask a teacher who has had allegations made against them, in certain situations, to agree to provide an 'undertaking not to teach' until the matter is resolved," the council said.
"It is a voluntary agreement between the teacher and the council that the teacher will not teach in the interim.
"If a teacher does not agree to an undertaking we may apply to the Disciplinary Tribunal for an interim suspension of their practising certificate."
The council said all investigations and cases it managed were confidential.
Details of investigations and cases weren't available to the public unless the case made it to the Disciplinary Tribunal, it said.
The school's board chairman confirmed one of its teachers had recently resigned.
"The school is working alongside the [Ministry of Education]
and the Teaching Council of Aotearoa New Zealand to ensure compliance with all our obligations as a school," he said.
The Ministry of Education's acting deputy secretary of sector enablement and support Jann Marshall said the school had notified her department.
"The school board is following the correct procedures, and we are supporting the school as they need," Marshall said.
"As is required when any alleged issue is raised about a person with a teaching registration, the board has informed the Teaching Council.
"The council now has a responsibility to consider whether or not an investigation of the person's suitability to continue to hold a teaching registration is warranted."
The man has built up a stellar reputation in his field and helped boost his school's teaching programme into one of the country's most respected.
A member of one organisation the man was involved with told the Herald on Sunday they were not aware of his alleged relationship with the student.
"We don't have any knowledge of this at all. I don't personally and as far as I know nobody else does," she said.
"So I think it would be a shock to hear this."
She said the matter was not related to her organisation, and declined to comment further.
