Prime Minister Giuseppe Conte also announced the closure of schools, gyms, museums, nightclubs and other venues across the whole country.
Baker told Morning Report the world had lost the fight to contain the virus.
He said figures over the weekend suggest a major tipping point for Covid-19 at the global level, but says New Zealand still has time to seriously ramp up efforts to contain the virus.
"We did pass these remarkable milestones on the weekend of more than 100,000 confirmed cases and more than 100 states and territories affected."
He said if containment doesn't work in New Zealand, we could face more 40 percent of the country getting infected with the virus.
"I think New Zealand, Australia, China and Singapore are showing that containment can work. I think the other remarkable milestone on the weekend was less than 100 cases in China for the first time in many weeks."
Baker said there were a lot of papers coming out of China showing how the virus was contained.
"Remember, this is not influenza, this is a different virus and I think now is the time for maximum containment effort in New Zealand.
"The game changer is that this virus can be contained and that means putting a huge amount of effort in and New Zealand has the opportunity, given that we've contained it so far, we can actually plan very pro-actively and very vigorously to do that."
He said silent transmission, where people get the virus but aren't diagnosed, is a potential problem in New Zealand and shows the need for rapid testing and contact tracing of everyone suspected of having the virus.
Baker said older and more vulnerable people did not need to change anything right now, but should plan for widespread community transmission by taking precautions.
"If we get widespread transmission, it will swamp health services everywhere - as we're seeing overseas - and that's why the containment process is so important."
Baker said the virus was likely to drag on for years as multiple epidemics overlap in different parts of the world.
"Parts of the world will come out of it sooner than others, particularly those that can get really organised. What we're going to soon see is a remarkable reversal - soon China will be putting restrictions on who can travel there, because they will have contained the virus."
He said the issue should not be politicised and there should be a Parliamentary group involving all parties to drive a consensus on how the country should respond.
Prime Minister Jacinda Ardern told Morning Report she was open to any suggestions that the National Party might have to curb the spread of the virus.
"This is a global issue, and a New Zealand issue first and foremost, not a political one."
Ardern said there were no new cases as of Monday morning.
New Zealanders travelling abroad are being urged to register with SafeTravel.
For the five cases confirmed, she said health professionals were already following up with contacts.
"Contact tracing is a critical part of containment," she said.
She said those who believed they were symptomatic should call ahead of visiting a GP to "reduce contact with health professionals".
Ardern said, at the point of a community outbreak, there would be notices issued to reduce large public gatherings.
"New Zealand is not at that point, but it always part of the planning to make sure you're ready to call that when it does," she said, adding "we are in containment".
Ardern said there was a system being developed to work with patients without them having to personally visit GPs, like "a Portacom in a carpark for instance".
"I want to make sure we have reach across the country."
She stressed good hygiene was one way to help the situation.
As for travellers from Italy and South Korea, she said the message to residents and citizens returning was clear: "Come to New Zealand only if you have the ability to successfully self-isolate."
"Our economic recovery relies on us getting the health response right. That's a primary focus. Secondly, we've had a lot of contact with those who are most heavily affected.
"We know there are specific areas that are affected so we are designing targeted responses. We will be talking about some of the definitive decisions we've made.
"Cash flow and keeping people attached to their jobs are the two most important focuses for us."
