The party is demanding an apology and review of standards and says it will complain to the Broadcasting Standards Authority.
The move follows a similar call for review by Kawea te Rongo, the Māori Journalists' Association.
The advert had featured on the Herald's front page on August 7, and said the foreshore and seabed must be "restored to public ownership", following on from government moves to amend the Marine and Coastal Area Act.
Te Pāti Māori and others have warned the move threatens to reignite the contentious foreshore and seabed debate and the marches that came with it.
In a statement, co-leader Rawiri Waititi said the advert was full of deceitful misinformation designed to sow resentment of Māori, and the party would "no longer engage with the New Zealand Herald after their disgusting attack".
"The New Zealand Herald have allowed themselves to be bought off by a well-resourced anti-Māori collective. They have promoted misinformation on their front page so they can feast off the anti-Māori agenda being pursued by this government," he said.
Co-leader Debbie Ngarewa-Packer said the party was demanding the Herald and its parent company NZME apologise to tangata whenua in all publications and radio stations, formally apologise for staff members and advertisers, review advertising standards including a robust plan to protect tangata whenua and a process for checking the accuracy of adverts.
"This is not about Hobson's Pledge. Their racism is well-known. It's about the integrity of the media and their moral obligation to the indigenous people of this land," she said.
"It's about their obligation to do their due diligence and uphold the truth."
