They have searched Wellington and Bowen Hospital in the capital and Burwood Hospital in Christchurch. RNZ understands police have also been at Auckland City Hospital.
However, Te Whatu Ora is reassuring people it is safe to attend hospitals as usual.
The Ministry of Education confirmed Auckland's Saint Kentigern College was evacuated as a result of the threatening email.
It would not reopen until police have given clearance.
Spokesperson Isabel Evans said the event can caused anxiety for school communities and ministry offices are open for schools who need assistance.
High school students are currently undertaking NCEA exams.
NZQA deputy chief executive of assessment Jann Marshall said the safety of students and staff was a top priority.
"Each school has its own processes for handling a security lockdown, and these apply during the exam period.
"Students who are unable to sit an exam, or whose performance is impaired because of a security incident, can apply for a derived grade, or their school may apply for derived grades at scale to apply."
PPTA acting president Chris Abercrombie said the primary concern of schools would be ensuring the safety of staff and students.
Police said staff were working with those impacted and would respond based on individual circumstances.
"Police acknowledge how unsettling these emails are for all concerned. We'd like to thank all involved for their cooperation as we investigate these emails."
Te Whatu Ora's national director for hospital and specialist services Fionnagh Dougan confirmed some hospitals received an "email of concern" earlier today.
"[It] was immediately referred to police for further investigation," she said.
"Staff have followed police advice and we are remaining vigilant. Our hospital sites have remained open and all services are continuing.
"Members of the public with appointments at our hospitals or needing emergency treatment should be assured it is safe to attend their local hospital as usual."
On 26 July 2022, some North Island schools went into lockdown and moved students off site after receiving phone threats.
Threats were made to five schools in Waikato, Thames Coromandel and Gisborne districts, police said.
No specific risk was ever found.
The next day, bomb threats were made to four schools and at least a dozen the next, causing widespread disruption with many of the schools having to evacuate.
The Principals' Federation said those threats originated from an overseas cyberbot.
