He said there are "a number of potential theories" about how the information was released.
But he wasn't willing to elaborate on any of these.
He said he has not been in touch with the people who had their information leaked.
He said officials involved have already looked at how this information was stored to make sure it can't happen again.
Heron's report will be back in "a matter of weeks, not months".
He said how many people had access to such a list will be looked at.
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He said the Government is still not aware of what format the information was released in - for example, if it was hard copy or online.
"We will be looking very closely at that."
There are other ministries involved other than the Ministry of Health, Hipkins said.
He said he was first made aware of the issue on Friday last week, when he was alerted to the issue by media.
"Our primary concern to is find out what happened."
He promised the Government would "get to the bottom" of how this information was made public.
"This is a serious matter."
Ardern said the leak was not political "at all".
She said there was "no politics in this".
Hipkins said the Government was handling this issue with "a great deal of importance".
Going forward, the Government will be making sure that if there is anything malicious going on, the Government will deal with that.
"We will do everything we can to get to the bottom of it," Hipkins said.
He said he does not think that information that gets sent to multiple media outlets can be characterised as an accident.
He would not go into detail about what the consequences of the person who leaked the information would be.
Only that it would depend who they were, and where they worked.
PM to attend funeral for slain officer
Ardern confirmed she would be attending the funeral for slain officer Matthew Hunt on Thursday.
The funeral will be at Eden Park.
The transtasman bubble
Ardern said New South Wales closing its border to Victoria was "entirely Australia's call" when asked about the transtasman bubble.
She would not go into details about the timing of the bubble, saying much of that was up to Australia.
He said if Australia opened up other states, then that "would be something we could work with," she said, about the bubble.
But, again, she would not provide a timeframe.
She said community transmission and testing levels are important in deciding on a bubble.
She said there would need to be separation of passengers on both sides.
Ardern confirmed that talks between New Zealand and Australian officials is still underway.
She said the status of some of the countries New Zealand was looking at in terms of a bubble, such as Australia, has changed - but at the same time, what New Zealand was looking for in terms of creating a bubble had not.
She said there is a Cabinet paper about this.
"It is important that we keep working with partners."
Ardern said that the last few months have demonstrated just how hard it is to keep a Covid-19 free environment.
She said officials were talking with Australian officials "as we speak" and this has been on-going for "some time".
But the last time she talked about Australian Prime Minister Scott Morrison was roughly two weeks ago.
'Spontanous' getaway' from quarantine
Asked about the woman who escaped from isolation, Ardern said it was "spontaneous".
The woman, who scaled two fences to escape from managed isolation facility last night, has been charged.
The 43-year-old fled on foot from the Pullman Hotel shortly before 6.20pm on Saturday.
The escaped woman was located a couple of blocks away by police on Anzac Ave at 8pm yesterday.
Ardern on Facebook and Kayne West's presidential bid
Ardern said she had no advice for US rapper Kanye West in his run for US President.
Ardern said it is her view that there is change that needs to occur on Facebook - she said the Government is working on forwarding that change.
"I still see there is an argument for those platforms to change," she said, adding that she would continue to hold them to account.
She said she wants work around violent extremists to ramp up.
But she said her decision not to do a Facebook Live was not going to meaningfully change anything.
Ardern said it was still her expectation that people be keeping digital diaries regarding their movements.
But she said the number of people using these had dropped off, but asked people continue to register their movements.
ACC levies on ice
Ardern said ACC levies will remain at the same level until 2022.
She said this will help levy payers in the "current environment".
This will cost the Government $278 this year, Ardern said.
Ardern said that New Zealanders can be assured that ACC is still in solid shape.
Minister Iain Lees-Galloway said ACC is in a "very very solid" position right now.
He said the most important thing is that it gives certainty to businesses.
He said ACC has been clear that it's hard to get the data to predict what the 2022 levies would look like.
Today's move will help give their analysis more time to figure this out.
Asked about cutting levies, he said the Government was "striking a balance".
