Outpatient appointments and patients coming for a non-urgent surgery have been affected.
Resident Doctors Association and Association of Professional and Executive Employees (APEX) national secretary Dr Deborah Powell says the cyberattack on the Waikato District Health Board appears to be a type of ransomware called "Conti".
It appears to be same type of attack that targeted Ireland's Department of Health last week.
Waikato District Health Board has set up a coordinated incident management system to try to resolve the situation as soon as possible.
A staff member at Waikato Hospital told RNZ it was chaos there as nothing was working.
"Some elective surgery has [been cancelled], some have still gone ahead, but some surgery has been cancelled," Waikato DHB chief executive Kevin Snee told RNZ's Checkpoint programme tonight.
"We're talking about a number of patients, but at this stage we can't be clear exactly how many because we're in the middle of it … it will only be clear about how many patients have been affected after the event.
"It's a cyber security breach. It's a virus that's affected our system and it looks like that's been malicious intent."
Snee said it could "well be" a ransomware attack.
"Certainly, the indications are that it is. We've received a message - we need to check the veracity of the message - but it appears to be indicating that it is a ransomware event.
"Obviously, when these events happen as they happen in other parts of the world, people are trying to extract money from an organisation. Clearly we will not be paying any ransom for this."
Snee said Waikato DHB received the message earlier today, and the attackers had not asked for a specific amount of money.
"We've had no threats [in the past]. It's a problem that we're aware of internationally and we've had problems in New Zealand before, but we've had no threats in relation to Waikato DHB.
"It's the whole computer system that we have a problem with at the moment. If there have been any security issues, that will be determined by investigation subsequently."
Snee said the DHB was working with cyber security experts from the Ministry of Health to find the source of the attack and rebuild the computer system.
He said they had made a number of improvements over the past year, and had not been told there was a problem.
Snee would not give details on what the attackers were demanding or if any further threats were made.
"It's a police matter, so I'd rather not go into it. We believe we've got it under control and we believe we'll have the services back up and running within a matter of days,
"We don't believe that any further problems will occur as a result of this… We're focused on patient care and getting the systems back up and running. That's what we intend to do. Irrespective of any further threats that may or may not happen, we will have the system back up and running."
The DHB is asking people to only go to Waikato Hospital Emergency Department for emergencies, so it can ensure it can continue to provide critical services to patients.
People trying to contact patients should consider using personal mobile phones where possible in the meantime, it said.
A union representing doctors said those working at Waikato hospitals and clinics had described the ongoing systems outage as "mayhem".
The Association of Salaried Medical Specialists said doctors had described how they were only going ahead with operations if they had printed patient notes.
The union said staff had been told the outage could take days to fix.
Meanwhile, Waikato DHB staff were told it was vitally important computers - including laptops - not be switched on again until further notice.
In an email to staff personal phones, Snee said all network-connected computers had to be shut down after the attack and getting through the next few days would require commitment and patience from all staff.
