There will be about 800 COVID-19 patients in hospital in under a week if numbers keep rising at the current rate.
There were 373 people in hospitals yesterday with the novel coronavirus and the system was already under strain.
Some services have been put on hold, operating theatres shut down and facilities temporarily closed.
There were almost 20,000 new community cases yesterday, but the impact that will have on the hospitalisation rate would be is a week away.
Plank said hospital numbers were doubling roughly every five days and if that continued, the number of people in hospital on 6 March would be close to 800.
However, the shape of the outbreak was very difficult to predict, particularly because the current high case numbers were partly due to delayed PCR results, along with new rapid antigen test results, Plank said.
"It could be that those numbers are starting to slow, and hopefully that is the case," he said.
"The models at the moment are suggesting that we could peak at around about 1000 people in hospital in about three weeks time but it does depend on what happens with cases."
Covid-19 Response Minister Chris Hipkins told Morning Report they had been working hard to avoid as many hospitalisations as possible.
"We are now in a phase where we are likely to see an increase in hospitalisations. One of our key focuses is the severity of those hospitalisations."
The peak of the outbreak was looking like it would be "sharp and short-lived", Plank told Morning Report.
"It's relatively short, it's probably a week or two of those really high numbers, and it will start to come down. It won't just sort of completely come down to zero, it will settle out at a lower level as we go through the rest of the year."
But Auckland's peak was expected to hit about a week ahead of other regions, which could be in a couple of weeks' time, he said.
Another scenario was the move to phase three - which had less contact tracing and fewer people isolating - could cause case numbers to rise.
It was possible, although less likely, hospitalisations would hit 2000 on any given day, he said.
Cases in the outbreak have so far skewed towards the younger age groups but if it virus crept at a higher rate into the older age group, it could potentially increase the numbers in hospital, he said.
"Now is possibly not the time to be visiting elderly relatives, visiting rest homes, that sort of thing, because we really don't want to see large numbers of infections in those groups."
RNZ
