Throughout the country, 493 people were in hospital with Covid-19.
The ministry also reported 24 people had died with Covid-19.
Auckland University Covid modeller David Welch said over the past week there had been a substantial rise in the seven-day rolling average of cases.
He said if a new wave was starting now, it was likely to peak towards the end of next month.
The modelling he'd seen suggested there could be 20,000 cases a day by that point.
Welch said if he was the Government he'd be closely watching the numbers, with a view to raising alert level settings.
Epidemiologist Michael Baker said while the single day jump nationally was large, it was the upwards trend in the weekly average cases and hospitalisations that signalled real trouble.
"Case numbers are always big on a Tuesday, because it picks up on the weekend tests – that pattern has been there for months that's why the moving average is so important."
With the moving average of Covid-19 cases being up by 1917, Baker said New Zealand could be in trouble.
"All the signs point towards a large wave of Covid-19 with an abrupt rise in cases, and it's very distinct."
He said Aotearoa should look to countries like Japan and Singapore for inspiration.
"They are mask-wearing societies, and there is also a big focus on staying home when you are sick, not going in to work – those are lessons we have not absorbed at all.
"We do need to act proactively rather than overwhelm the hospitals – so isolation periods, mask wearing and things like that."
