Lawyers are seeking clarification from the Chief Justice after the Prime Minister raised the Covid-19 alert level to 3 with level 4 to follow in 48 hours.
The country is going into lockdown for at least four weeks to control the spread of the global coronavirus pandemic.
Prime Minister Ardern announced this afternoon that schools, childcare centres and universities will be closed from Wednesday.
All non-essential businesses or services must also shut in the next 48 hours and Kiwis should stay at home unless visiting an essential service.
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Ardern said the strict measures will save tens of thousands of lives.
The New Zealand Law Society has sent a message to Chief Justice Dame Helen Winkelmann asking what this will mean for the country's courts and justice system.
"We know you are all anxious following the Prime Minister's announcement today," the Law Society said in tweet.
"The NZBA (New Zealand Bar Association), CBA (Criminal Bar Association), and Law Society | Te kāhui Ture have sent a joint communication to the Chief Justice seeking clarity and a further response on court protocols. Updates to come."
The Chief Justice had already ordered a halt to any new jury trials for at least two months due to Covid-19.
But, she said in a letter to New Zealand's legal profession last night, that the country's courts will remain open.
Proceedings will be prioritised, the Chief Justice added, and the number of people allowed in courthouses will be limited.
The Ministry of Justice is also ordering infrared scanners to test people's temperatures when entering a courthouse. Those who appear to have a fever will be turned away.
Many judicial decisions will now also be made on paper and some hearings conducted by telephone or video, the Chief Justice said.
At the Ministry of Justice, many staff are already working from home.
In a statement, Secretary for Justice Andrew Kibblewhite said the ministry was working closely with the Ministry of Health on the Covid-19 situation "to ensure the health, safety and wellbeing of our people, the Judiciary and all court users".
"We have met with the Judiciary to plan for how court business and justice services will continue in the coming weeks," he said.
"As the Chief Justice has announced, all courts and tribunals will be open today. Criminal court matters will continue."
However, Kibblewhite said those aged 70 or over, are pregnant, or are undergoing treatment for cancer or a blood condition, should not attend their court hearing.
"Please also remain home if you are self-isolating or caring for a vulnerable family member. Call 0800 COURTS to advise them of your circumstances," he said.
Kibblewhite said he wanted to assure court participants the court buildings were being cleaned regularly and asked all participants to please wash their hands thoroughly, keep a reasonable distance from other participants where possible, and cover their nose and mouth if you cough or sneeze.
"I ask all court participants to be kind, to be patient, and to bear with the ministry and the Judiciary as we navigate these uncertain times.
"As for staff at the Ministry's National Office in Wellington, only those who are currently considered critical to maintaining the justice system in light of the current circumstances will be in the office. All other staff have been asked to remain home unless their manager requires them in the office for these critical services."