"This is an invasion of our family's privacy and it is a pity that @georgefmnz has allowed itself to be part of and endorsed @thanekirby's idiocy."
In a statement released to the Herald, George FM said the segment was intended to be "fun" but admitted it was the wrong thing to do.
It said there was "no plan or intention to film Lorde".
"Knocking on Lorde's door was an off-the-cuff moment of live radio intended to be light hearted and fun. There was no malicious intent, but George recognises the moment was inappropriate and ill-advised.
"Apologises were made to Sonja Yelich and her family yesterday, both on air and in a formal letter."
Lorde has become the target of paparazzi attention since her single Royals hit No. 1 in the US and won two Grammys last year.
Photos of her swimming at the beach with her boyfriend James Lowe have appeared in local gossip magazines, while TMZ recently posted photos of her hiking with Taylor Swift.
This time last year, Lorde slammed a waiting media scrum that greeted her at Auckland airport, saying she was under a "constant, often lecherous gaze" and said she no longer felt safe in her "tiny home country".
In a series of tweets that she deleted soon after, she wrote: "i understand that people of note are supposedly fair game for everyone to photograph and film but that doesn't make it acceptable.
"i'm beginning to get used to my image as a public commodity, and the fact that I'm getting used to it frightens me.
"there is a difference between attn from fans, which i love, and the constant, often lecherous gaze that i'm subjected to in this industry.
"i know that success comes with a price tag. it just sucks when you see that in your tiny home country where you previously felt safe."
- nzherald.co.nz