It comes as part of a wider global move, as various other OECD countries explore similar taxation options.
Ardern said highly digitalised companies, such as those offering social media networks, trading platforms, and online advertising, currently earned a significant income from New Zealand consumers without being liable for income tax.
"That is not fair, and we are determined to do something about it."
And National agrees – the party's finance spokeswoman Amy Adams said National thought multinational should pay their fair share of tax.
Companies likely to be hit by such a tax include the likes of Facebook, Google and Twitter.
The value of cross-border digital services in New Zealand is estimated to be roughly $2.7 billion.
New Zealand is not the only country concerned about big digital companies not paying enough tax – the OECD has been trying to find an internationally agreed solution for years.
Although Ardern said progress had been made, it could still take a number of years for a tax solution to be reached and this tax was an interim until a more globally focused alternative was agreed.
New Zealand companies pay a 28 per cent tax on their profits, but nothing on revenue.
The companies likely to be hit with the new tax do not pay company or income tax.
Revenue Minister Stuart Nash would not name which companies he expected to be hit by a tax such as this but said it would be "obvious" who would be targeted – citing social media companies as an example.
The Government's announcement comes as it faces questions over another multinational company, Huawei, and its bid to help Spark build a 5G network in New Zealand.
The Government's spy agency, the GCSB, banned Spark from using the Chinese telecommunications giant's gear, warning it could raise a significant national security risk, according to Spark.
New Zealand shares yesterday edged slightly lower as fears over the country's trade relations with China unnerved investors. New Zealand's benchmark index was one of the few to decline across Asia, dipping by 0.2 per cent.
Addressing media yesterday afternoon, Ardern said Cabinet agreed to issue a discussion document in relation to the new tax, which would seek feedback on any proposed changes to the way multinationals were taxed.
It will be released in May, Nash said.
New Zealand's move comes as a number of other countries also consider reassessing their approach to the taxing of multinationals.
Ardern listed a number of countries which were looking at a similar tax, including Australia, the UK, France Spain, and Austria. India has also decided not to wait for the OECD.
The proposed tax in France, for example, is a levy on all internet direct sales, advertisements and the sale of private data.
But similar measures are being discussed by the US, the European Union and the United Kingdom are limited to online advertising
Although welcoming the taxing of multinationals more, Adams said a country as small as New Zealand would find it difficult to go out on its own.
"We support the OECD work being ramped up. The solutions to these problems is best achieved by countries working together."
A Herald 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.
A taxation timeline
October 2016 – The "Netflix Tax," which requires companies to pay GST on digital services, such as e-books, music and video downloads, came into effect.
July 2018 – BEPS, a law which stopped global companies with a New Zealand presence from aggressive tax planning such as shifting profits earned overseas to reduce their tax liability, came into effect in July, 2018.
February 2019 – The Government announces plans to tax on the revenue of multinational digital companies, likely to be between 2-3 per cent.
October 2019 – The "Amazon Tax," which requires foreign companies to collect GST on low-value products bought online in NZ, is due to come into effect in October this year.
