Dorsey said this was not right when it comes to politics.
"A political message earns reach when people decide to follow an account or retweet," he said on Twitter.
"Paying for reach removes that decision, forcing highly optimised and targeted political messages on people. We believe this decision should not be compromised by money."
He said while internet advertising is incredibly powerful and very effective for commercial advertisers, that power brings significant risks to politics, where it can be used to influence votes to affect the lives of millions.
Asked about Dorsey's decision this morning, Prime Minister Jacinda Ardern said it was up to all political parties to adapt to online platforms.
When it comes to political advertising, social media is still a relatively new phenomenon, she said, adding "we will adapt as the rules change".
"Ultimately the most important thing is that people are able to access clear and definitive information and they weed out misinformation and people can actually rely on what they see during political campaigns."
National is not worried about Twitter's decision.
"We don't advertise on Twitter and hadn't intended to during the campaign. Twitter can make their own decisions on who can advertise," the party's campaign chair Paula Bennett said.
Twitter's decision now puts the pressure on other social media platforms, such as Facebook and Instagram (owned by Facebook).
Facebook has already faced heavy criticism after its founder and chief executive, Mark Zuckerberg, decided that politicians would be allowed to post ads on the social media platform which include false claims.
Technology and social media commentator Paul Brislen said it was easy enough for Twitter to take the high ground on this issue because the way it advertises is different to Facebook.
And it's Facebook, he said, which needs a closer look when it comes to political ads, particularly around micro-targeted ads – a technique that involves targeting people based on their online activity (such as liked pages).
"There's a huge potential area there that needs to be rigorously enforced by our Electoral Commission and I'm unsure as to whether they've thought about it or not.
"Facebook's willingness to allow political parties to tell lies in their advertising flies in the face of New Zealand's electoral regime and that's of great concern."