Four Auckland schools have been linked to confirmed Covid-19 cases in the past day, as the number continues to climb nationally.

Marist College, Randwick Park School and Glendowie College have all shut their doors following confirmed or probable cases of coronavirus linked to staff and students.

The father of a Mt Roskill Grammar Student has also tested positive for the virus, but the school has not announced that it will close.

A student at Randwick Park School is a "probable case" of Covid-19, with their test results expected back late Sunday night, parents were told.

"We consider it highly likely to show Covid-19 infection," an email to parents said.

The school is shut until the results return, and will remain closed for a further 72 hours if the case is confirmed, to allow for cleaning and contact tracing.

"Please be assured that the person, and their whole household, are now in self-isolation.

"They are being supported at home and will only return to school after they have completed their isolation period and are well."

A Glendowie College student was diagnosed with coronavirus, triggering a lockdown beginning tomorrow while close contacts are traced and put into self isolation.

The letter to Glendowie parents says the student and their whole household are now in self-isolation.

"They are being supported at home and will only return to school after they have completed their isolation period and are well."

Close contacts will be required to self-isolate for 14 days, the letter says.

Principal Richard Dykes told parents contact tracing would start today and he and the deputy principals would be at school from this morning (Monday) to work on this process. No other staff would be at work.

"Until then, I recommend that you keep your child[ren] at home until we confirm whether they have been in close contact with the student," Dykes wrote. "This will be the school's first priority."

At Mt Roskill, the infected parent arrived in Auckland from Europe on March 12 and attended the Tongan Fiafia event at the school that night for about an hour, the letter from principal Greg Watson told parents.

New rules requiring international travellers to self-isolate for 14 days were brought in several days after he arrived in New Zealand.

His child attended school most days following until March 19 and does not have symptoms, Watson said.

The school has sought "urgent advice" from the Ministry of Education and the Ministry of Health.

Mt Roskill Intermediate principal Kristen Walsham told the Herald the three schools on the Mt Roskill campus - Mt Roskill Grammar, Mt Roskill Intermediate and Mt Roskill Primary - were awaiting further advice from the Ministry of Health and the Ministry of Education on the contact tracing process and what actions people should be taking.

"We will communicate with close contacts as soon as we have tracked and identified them. We will then contact all other students to advise that they have not been in close contact."

Marist College, a Catholic girls' high school in Mt Albert, earlier announced that a staff member had tested positive for Covid-19.

The school is expected to reopen on Thursday after extensive cleaning and contact tracing, parents were told.

The staff member and her whole household was now in self-isolation, the letter said.

"They are being supported at home and will only return to school after they have completed their isolation period and are well."

Principal Raechelle Taulu told the Herald the school's priority was to "wrap around" the woman to make sure she had all the support she needed and to support other staff and the school community.

"We have been planning for this in terms of being prepared for students to work remotely from home - like many schools," Taulu said.

Neighbouring Marist Primary School has also closed for a minimum of 72 hours as a precaution.

The Catholic school told parents the board had decided to close because of family links between the two schools and interactions between staff and students.

A skeleton staff will remain at the primary school for parents who could not make arrangements straight away or for children of essential workers like health, emergency and supermarket workers.

The spate of school infections come as 14 new cases of Covid-19 in New Zealand were announced today, bringing the total to 66.

At her first-ever address to the nation on Sunday, Prime Minister Jacinda Ardern introduced a four-tier alert system, based on the spread of Covid-19.

New Zealand remains at alert level 2, meaning the virus is contained but the risks are growing. Affected schools may close at level 3, with all educational facilities to shut if level 4 is declared.