It is understood Aden was accompanied by police this morning, The New Zealand Herald understands.
Prime Minister Jacinda Ardern announced last month that Aden and her children would return to New Zealand from Turkey, where they have been held by authorities since crossing the border from Syria.
Aden was born in New Zealand but moved to Australia when she was six, travelling to Syria in 2014 on her Australian passport.= But Australia cancelled her citizenship - forcing responsibility for her onto New Zealand.
Asked about Aden's return at today's 1pm Covid-19 media update, Ardern said she would not be commenting publicly on the case for "a range of reasons, not least security reasons".
Asked if Aden would be mixed in with other managed isolation and quarantine guests, the Prime Minister said they were maintaining all the usual quarantine procedures.
"I think the most important point for me to make is we are undertaking all of the usual Covid-19 related protocols for someone who has come in from a country that has Covid in circulation. That is essentially anywhere in the world at the moment so we will follow those same protocols."
Asked what assurances the PM could give to the public about their safety, she said authorities have "used every level we have" to make sure there is little risk to New Zealanders.
"I would give the same reassurance that I have all the way through, that while we have obligations given that this individual we are talking about is a New Zealand citizen, and of course the status of their children, we have still undertaken all of the usual steps that you would expect us to keep New Zealanders safe. That has been an absolute priority.
"Whilst there is some constraint on my ability to talk about the details of those, I can tell you that we have used every level we have to ensure people's safety."
Ardern objected to the suggestion that she was asking New Zealanders to trust her without giving any details. She said trust was being asked of "not me, but our systems".
She would not say whether more details on Aden would be released further down the line.
"No, the key test for me is this: my job is to keep people safe, and we are using all of the levers that we have to make sure that we have done everything we can to keep people safe while at the same time fulfilling those obligations we have.
"Because this is a New Zealand citizen. There isn't really an option here. The alternative would have been to say to Turkey that we don't take responsibility and they could have then deported that person without warning and without our preparation. That would have been wrong.
"That would not have ensured the safety of New Zealanders. So we've planned for it, we're ready for it, and we are keeping in mind here there are also children involved that we have an obligation to as well."
Aden lived in New Zealand until age 6, when she moved to Australia. She travelled to Syria in 2014, where it is alleged that she joined Isis, married two of the terrorist group's fighters and had three children.
Her case has been a bone of contention between Ardern and Australian Prime Minister Scott Morrison, after Australia stripped her of Australian citizenship without giving notice to New Zealand.
Morrison had described Aden as "an enemy of our country", while Ardern had argued that the family's support base was in Australia and that was where they should return.
