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Photographs in Woman's Day show a bikini-clad Lorde perched on her boyfriend James Lowe's shoulders as they frolic in the sea. In other photos, the young couple are hugging, and enjoying the view from a lighthouse.
Mau said the young Kiwi singer should be safe from that sort of intrusion in her home country.
"Do we as Kiwis want New Zealand to be a place where Lorde can come home to, and feel safe, and enjoy her privacy? I very passionately do," Mau told the Herald.
Mau said Woman's Day had crossed the line. She said the pop star should be left alone and spared intrusive media glare.
"Lorde may be wise beyond her years, but she is still a minor. The fact that she's a double Grammy winner and a celeb is a red herring. She is still under 18 and deserves to be able to grow up and form relationships without being followed by photographers taking photos of intimate moments with her boyfriend.
"Woman's Day will say, 'She looks gorgeous in a bikini, and we're just celebrating the love between Lorde and her boyfriend,' but bulls***! They printed the titillating photos in the magazine for the sole purpose of selling more mags."
Paul Dykzeul, chief executive of Woman's Day publisher Bauer Media, said: "Frankly why would we be concerned about what someone like Ali Mau thinks? We care about readers, and these photos would be and are of genuine interest to our readers.
"Lorde is an extraordinary talent that all Kiwis should be proud of. Naturally people are interested in her life."
He said Mau had a "long-standing dislike" of the magazine.
Other paparazzi photos taken this week by international agencies, showing the Kiwi teenager and her friends shopping in Hollywood the day after her Grammy wins, were published in Britain's Daily Mail and on international gossip websites.
This week, Lorde criticised New Zealand media for almost pushing over her family during her arrival at Auckland Airport, calling it "a bit of a sad welcome" in a flurry of tweets that were later deleted.
Lorde was unavailable yesterday and her manager, Scott MacLachlan, was unwilling to be dragged into Mau's debate.
"I don't have any comment about those pics," he said.