The man in hospital had been isolating at the Haka Hotel in Auckland, the ministry said.
He arrived in New Zealand on June 24 on flight AI1316.
"Following the onset of symptoms, he was taken by ambulance to Auckland City Hospital last night and was tested for Covid-19 as part of a clinical assessment. He remains in the hospital in a stable condition on a ward and has not required ICU level care," the ministry said.
"Members of staff treating the man were made aware that he had returned from overseas to a managed quarantine facility and appropriate protocols were followed, including the use of PPE. No members of staff are considered close contacts.
"The patient was cared for in a separate room in the clinical assessment unit at Auckland City Hospital before being transferred to a separate room on one of the hospital wards."
Of the other three cases, the first is a woman in her 30s who arrived in New Zealand from India on June 14.
"She is the wife of a previous case who tested positive on June 21 and had been isolating separately from her husband since his positive test. She was considered a close contact and tested positive on day 11 of her stay," the ministry said.
"The second case is a man in his 30s who arrived from Nepal via Sydney on 18 June (flight NZ102).
"He tested positive on day three of his time at the Novotel Ellerslie. Three close family contacts of the man travelling with him have also been tested, with two negative results and a third pending. All are being treated as close contacts so will be checked daily and retested if they develop symptoms or at day 12 of their stay.
"The third case is a man in his 30s who was in isolation at the Grand Millennium hotel. His result also came as a result of day three testing. Further details are being established by Auckland Regional Public Health."
The ministry said Auckland City Hospital had "considerable recent experience of treating patients with Covid-19" and it was "safe for patients, visitors and staff".
Director general of health Dr Ashley Bloomfield said the new cases reinforced the "critical importance" of spending 14 days in managed isolation or quarantine together with daily symptom checks.
"Even with all arrivals being tested twice during their stay in managed isolation, we also continue to do a daily check for symptoms consistent with Covid-19 as part of our broader programme, which includes strict protocols in our managed isolation and quarantine facilities," he said.
"While today's news that one of our recent cases is in hospital may be concerning to some, it is something the health system in New Zealand has remained prepared for. This person is receiving good treatment from the team at Auckland City Hospital who have previous experience of managing positive cases."
New Zealand's confirmed number of Covid-19 cases is now 1176.
Yesterday, 5321 tests were completed in laboratories, bringing the total number of tests to date to 392,756. This includes testing at managed isolation facilities and community-based testing across the country.
The ministry said that "of the 2159 people who left managed isolation facilities between June 9 and June 16, 1253 people have been contacted and have tested negative for Covid-19; 800 of those were tested before leaving managed isolation and the remaining 453 were tested after departure from the facility".
They said 342 people "have been referred for a test that we are awaiting results for. There are 427 people who we have repeatedly tried to make contact with, including via text and via phone calls.
"As needed we will refer people we do not make contact with to finding services. Ninety-two of these had invalid phone numbers, so have already been referred to finding services.
"We have had 137 people who will not be tested because of reasons such as being a child, being part of repositioning crew, currently being overseas or they are refusing a test. Seventy nine people have refused testing."
Today's Ministry of Health update on whether there are any new cases of Covid-19 in New Zealand was via a media statement.
The full statement:
Today there are four new cases of Covid-19 at the border. There continue to be no cases in the community.
All four cases involve people who have recently returned from overseas and were in managed isolation facilities.
These cases bring the number of active cases in New Zealand to 20.
Three of today's cases are now in quarantine at the Jet Park facility in Auckland. The fourth is in Auckland City Hospital in a stable condition. All appropriate precautions are being taken.
The first case is a woman in her 30s who arrived in New Zealand from India on 14 June. She is the wife of a previous case who tested positive on 21 June and had been isolating separately from her husband since his positive test. She was considered a close contact and tested positive on day 11 of her stay.
The second case is a man in his 30s who arrived in New Zealand from Nepal via Sydney on 18 June (flight NZ102). He tested positive on day three of his time at the Novotel Ellerslie. Three close family contacts of the man travelling with him have also been tested, with two negative results and a third pending. All are being treated as close contacts so will be checked daily and retested if they develop symptoms or at day 12 of their stay.
The third case is a man in his 30s who was in isolation at the Grand Millennium hotel. His result also came as a result of day three testing. Further details are currently being established by Auckland Regional Public Health.
The fourth case is a man in his 30s who was isolating at the Haka Hotel in Auckland, having arrived in New Zealand on 24 June on AI1316. Following the onset of symptoms, he was taken by ambulance to Auckland City Hospital last night and was tested for Covid-19 as part of a clinical assessment. He remains in the hospital in a stable condition. and has not required ICU level care.
Members of staff treating the man were made aware that he had returned from overseas to a managed quarantine facility and appropriate protocols were followed, including the use of PPE. No members of staff are considered close contacts.
The patient was cared for in a separate room in the clinical assessment unit at Auckland City Hospital before being transferred to a separate room on one of the hospital wards.
Auckland City Hospital has considerable recent experience in treating patients with Covid-19. Members of the public can be assured that the hospital is safe for patients, visitors and staff.
As we said yesterday, the Covid-19 pandemic continues to accelerate overseas and new cases were always expected at our border.
Our strict border controls, in particular, the 14-day stay in managed isolation or quarantine, ensure that arrivals are managed with appropriate public health protocols and isolated from other New Zealanders while they may be incubating the virus.
"What these cases once again reinforce is the critical importance of these 14 days spent in managed isolation or quarantine together with daily symptom checks," says director general of health Dr Ashley Bloomfield.
"Even with all arrivals being tested twice during their stay in managed isolation, we also continue to do a daily check for symptoms consistent with Covid-19 as part of our broader programme, which includes strict protocols in our managed isolation and quarantine facilities.
"While today's news that one of our recent cases is in hospital may be concerning to some, it is something the health system in New Zealand has remained prepared for.
"I want to reassure the wider community that this person is receiving good treatment from the team at Auckland City Hospital who have previous experience of managing positive cases."
Our total number of confirmed cases of Covid-19 is now 1176, which is the number we report to the World Health Organisation.
Yesterday our laboratories completed 5,321 tests, bringing the total number of tests completed to date to 392,756. This includes testing at managed isolation facilities and community-based testing across the country.
Of the 2159 people who left managed isolation facilities between June 9 and June 16, 1,253 people have been contacted and have tested negative for COVID-19; 800 of those were tested before leaving managed isolation and the remaining 453 were tested after departure from the facility.
342 people have been referred for a test that we are awaiting results for.
There are 427 people who we have repeatedly tried to make contact with, including via text and phone calls. Again, a reminder to anyone who was in a managed isolation facility between June 9 and 16 who has not yet spoken with Healthline to call the dedicated team on 09 302 0408.
As needed we will refer people we do not make contact with to finding services. 92 of these had invalid phone numbers, so have already been referred to finding services.
We have had 137 people who will not be tested because of reasons such as being a child, being part of repositioning crew, currently being overseas or they are refusing a test. 79 people have refused testing.
NZ COVID Tracer App
NZ Covid Tracer has now recorded 583,000 registrations.
We continue to encourage as many people as possible to download and use the app ‐ this will support our contact tracing efforts in Level 1.
It's great news that more and more businesses and organisations are displaying their official QR codes. The number of posters created by businesses is now 75,316.