"That is not fair," Ardern said, adding that the Government is determined to do "something about it".
She said the current tax system was not sustainable and it's a gap this government thinks should close.
She said a number of other countries are looking at similar taxes, such as Australia and certain European countries.
International tax rules have not kept up with modern business, Revenue Minister Stuart Nash said.
Although they said they didn't want to name any companies, Nash said it would be reasonably obvious as to what companies would be targeted – citing "social media companies".
Nash said the interim measures would be in place by 2020.
Ardern said cabinet had been been discussing this for some months.
Ardern said the tax would be 2-3 per cent - in line with that of other countries that have looked into a similar tax.
Several tax advisors spoken to by the Herald this afternoon, who declined to speak on-the-record due to the imminent announcement, said the move had taken them by surprise.
One said while he was blindsided, it was understandable Inland Revenue would prefer to keep its plans under wraps to avoid multinational companies restructuring their affairs in advance to avoid such a new tax.
"I do have some sympathy for them doing it secretly," the tax advisor said.
The move follows the introduction of a similar tax in France, and a report last month by the OECD's Base Erosion and Profit Shifting (BEPS) working group that the challenges faced by the increasing digitalisation of the global economy would this year be a key area of work.
The proposed tax in France is a levy on all internet direct sales, advertisements and the sale of private data. Similar measures being discussed by the European Union and the United Kingdom, are limited to online advertising. Proposed levies have ranged between 2 and 3 per cent of annual revenues.
"It raises questions of where tax should be paid and if so, in what amount in a world where enterprises can effectively be heavily involved in the economic life of different jurisdictions without any significant physical presence," a recently-issued BEPS policy-note says.
The issue - of multinational companies selling goods or services online, and booking revenues in low-tax jurisdictions or charging local subsidiaries high licence or service fees - has been bubbling away in New Zealand for several years.
Nash said the Government would receive $30-$80 million a year in revenue, depending how it is designed, if the tax goes ahead.
She said the Government was sure that the introduction of this tax would not impact New Zealand companies.
"New Zealand is currently working at the OECD to find an international agreed solution for including the digital economy within fax frame works," Nash said.
Ardern said she was not concerned that the bigger companies would decide to leave New Zealand, as a result of such a tax.
"International tax rules have not kept up with modern business development," Ardern said.
"In the longer term, this threatens the sustainability of our revenue base and the fairness of the tax system."
At the moment, the value of cross-border digital services in New Zealand is estimated to be roughly $2.7 billion.
"We are determined to ensure that multinational companies involved in this sector of the economy pay their fair share of tax," Ardern said.
Asked if tax experts and companies in the industry were consulted, Ardern said no.
That was what the upcoming discussion document was all about, she said.
National's finance spokeswoman Amy Adams said:
"We agree multinationals should pay their fair share. That's why we started New Zealand's work on Base erosion and profit shifting (BEPS). However, a country as small as New Zealand would find it difficult to go out on its own without our citizens missing out on much the global market has to offer. We support the OECD work being ramped up. The solutions to these problems is best achieved by countries working together."
The Herald tax gap investigation into corporate tax avoidance in 2016 found 20 of the most aggressive multinational companies recorded $10b in annual revenues but collectively paid less than $1.8m in corporate income taxes.
The series also found Facebook and Google had structured their affairs to avoid a taxable local presence, instead using New Zealand subsidiaries to offer only marketing services with sales to Kiwi businesses for advertising - amounting to hundreds of millions of dollars a year - routed to other subsidiaries in low-tax countries like Ireland or Singapore.
According to the company's most-recent financial results, Google paid just $392,917 in tax a year, while Facebook paid only $43,261.
Partly in response to global public and political pressure, both these companies announced last year they would no longer book locally-sourced revenue offshore.
The Tax Working Group - whose final report is due to be made public on Thursday - in their interim report in September described such a move as a "equalisation tax".
"An equalisation tax would be a way to collect some tax from some digital companies that have been paying little tax in New Zealand or overseas. It would also help to signal the increasing urgency of the problem, and New Zealand's determination to find a solution," the report said, citing the risk the measure could cut against existing trade obligations.
