The Covid-infected man visited the newborn child and his partner twice, while potentially infectious.
The mother returned a negative test result and the baby tested positive yesterday.
The man's partner and their newborn child had been in a single room – separated from other mothers and babies – for the duration of their care.
"They have been relocated to a Covid-appropriate ward and safety protocols are in place," Waitematā District Health Board says.
The maternity ward remains fully operational - however some hospital staff have been stood down.
"The safety of our patients, their visitors and our staff is paramount. Work is rapidly underway to fully assess the situation and determine if further actions are required.
"A limited number of staff who have potentially interacted with the visitor have been stood down as a precautionary measure while investigations continue."
More household cases in Raglan
Meanwhile there are more Covid cases in Raglan - with household members of the first case confirmed overnight, Prime Minister Jacinda Ardern says.
And while a move out of level 3 for Auckland this week now seems highly doubtful - following the spread of Delta to Raglan and Hamilton - Ardern indicated this morning there could be the easing of some restrictions for the region, as experts study the granular detail of how cases are spreading.
She also signalled that New Zealand's Covid elimination strategy is coming to an end - describing the move to vaccinate as many people as possible as a "transition" phase.
Ardern's comments follow the announcement of 33 new cases yesterday - and, more significantly, the two new cases outside of Auckland, in Hamilton and Raglan. Those two cases are known to each other and Ardern confirmed this morning genome sequencing had linked the Hamilton case to the Auckland outbreak.
The additional Raglan household cases have been transferred to quarantine but there have been no positive cases attached to the Hamilton case or the case of the Auckland truckie who tested positive and was in Palmerston North.
Asked on RNZ if the Waikato cases meant a ruling out of level 2 for Auckland this week, Ardern said: "Movement there isn't material to that decision.. for us it is still around the nature of the outbreak itself in Auckland.
"I know that people naturally look to singular alert level shifts. What we've been doing instead is just looking across the board at all of the restrictions. And looking at whether or not there are some options that are lower risk that we could ease just to support Aucklanders."
She said details of Auckland's road-map would be outlined at 4pm today and she did not want to pre-empt any Cabinet decisions ahead of that.
But there were other options than simply moving to level 2. "We want to give a bit of a sense of the longer term for Auckland."
Experts could also study the granular details of what was causing the spread of the current cases - and whether they were attributable to certain restrictions "and therefore make a determination of what we consider high risk versus lower risk options around supporting Aucklanders".
On the elimination strategy, the Prime Minister said: "I think we've always used elimination in the right way at the right time and you'll hear me talk a little bit about this, this afternoon. But the reason - seven weeks ago at the beginning of this outbreak - that we said look we're sticking with elimination, we're using the lockdown was very much because we saw that we haven't got enough people vaccinated yet to take an alternative strategy."
Just under 79 per cent of New Zealanders have received at least their first jab - experts say the country needs to be at least 90 per cent vaccinated to control the Delta virus.
"We are still vaccinating," Ardern said. "We still don't want a widespread, uncontrolled outbreak with exponential growth, because we still need to continue to vaccinate people. But what I'll try and signal today is just what does it mean for the future for both Auckland and New Zealand during that transition period."
Asked whether that meant the elimination strategy was at an end, she said: "We're in a transition. So we are changing our strategy as we move. We still need to control this outbreak but we are transitioning."
Waikato case linked to Auckland
Genome sequencing had linked the Hamilton case to the Auckland outbreak - Ardern said she would leave it to scientists to work out if there were enough clues in the sequencing to figure out what had happened.
Asked how the soft border in the Waikato would work, she told The AM Show that the hard border was needed in Auckland because the outbreak was widespread. But even border checks didn't make that iron-cast - it was not a guarantee.
Level 2 in other places was because of the possibility of the virus getting out.
The soft border in the Waikato was "pragmatic".
Asked if elimination would not ever happen in Auckland, Ardern said the road-map would be announced at 4pm for Auckland, "keeping in mind that ... we do need to continue to be really cautious".
Vaccines were making a difference to this outbreak but it's about what happened in coming weeks, she said.
A short, sharp change in alert levels could be potentially dangerous.
Asked if it would be a "Sydney style" opening up at a particular vaccination target, Ardern said not necessarily - New Zealand had a different situation than New South Wales.
"Don't expect these big lurches in alert level changes" - Auckland could expect smaller changes.
Meanwhile, Deputy Prime Minister Grant Robertson told Newstalk ZB today that work was under way to find out how Delta had leaked into the Waikato and it was hoped whole genome sequencing would give answers. Officials should get that information sometime today, he said.
Robertson wasn't ruling out unlawful activity - such as a Covid-positive person crossing the border without permission.
