Hipkins says whole genome sequencing received last night shows the Auckland Airport worker, who tested positive for Covid-19 yesterday, is linked to a case that arrived on the 10 April.
The ministry has confirmed the cleaner did clean the plane that the other case arrived on.
Last night the ministry said 16 close contacts of the airport worker had been identified.
All tests so far of contacts for the plane cleaner have come back negative, Hipkins says.
The ministry previously said Auckland Airport was the person's sole employer, and their role was non-public-facing.
Prime Minister Jacinda Ardern has previously said the worker was fully vaccinated, but added that people could still get Covid-19 despite that.
The new case came just one day into the start of a quarantine-free travel bubble for Australia and New Zealand.
In this afternoon's Covid update, Hipkins also confirmed he has received his second Covid-19 vaccine.
He says 183,351 doses of the vaccine have been administered to date, 140,580 people have had a first dose, and 42,771 have had a second dose.
Some 41 per cent of first-dose vaccinations were in Auckland, 19 percent of whom are Māori or Pasifika, he says.
Vaccinations have been across 142 different sites with about 1200 vaccinators so far. More than 2500 people have completed the vaccinator training.
Across New Zealand, 12,697 Māori have received their first vaccine, with 4343 of those having also received a second dose.
Hipkins says of the 16314 of the estimated 50,000 border workers' family contacts have been vaccinated.
"I would like that number to be higher ... please do come forward and get those vaccinations."
He also addressed the anti mask wearing flyers that have been distributed particularly on public transport in Wellington.
“They've been handing out mask exemption cards that are based on the official exemption cards that area avail to those who need them and they are handing out a pamphlet which whilst it looks professional has a lot of information in it that is factually wrong and potentially dangerous."
He suggests the best place for the flyers is in the rubbish bin, saying they are highly disrespectful to the people who genuinely need an exemption to wearing a mask such as a health or disability reason.
Dr McElnay says there are no new cases of Covid-19 in the community and there is one border case that arrived from Switzerland via Qatar on April, 16.
The border worker who contracted Covid-19 from cleaning a plane has been moved to a quarantine facility in Auckland.
She says 25 close contacts have been identified and seven of those have tested negative so far.
One contact is being followed up today, and the remainder of those identified are not yet due for testing - this is because we test close contacts on day 5 after they have potentially been exposed to the virus for the best chance of detecting any infection that may be incubating, she says.
All close contacts are self-isolating.
Of those, 17 are workplace contacts. This number will likely increase – the person worked three shifts during their infectious period with a number of colleagues, and officials are working to determine who is a close contact from their interactions, says Dr McElnay.
The whole genome sequence was indistinguishable from that of a person who arrived in the country on 10 April from Ethiopia via the United Arab Emirates. The genome of both these cases is the B.1.1.7 – which is the variant first identified in the UK.
We have confirmed the worker announced as a case yesterday did clean the same plane the person from Ethiopia arrived on, she says.
“While there is a clear link to a known case of Covid-19, we are still investigating how the cleaner was infected.”
She asked people to please take a vaccine when they are offered it, to protect them and their family.