The performances had been scheduled for early next year but have now been postponed until early 2023.
He has also announced the newly rescheduled North American Farewell Yellow Brick Road dates, to begin in New Orleans on 19 January, 2022.
This will follow the recently rescheduled European dates, beginning in Berlin on September 1 next year.
The 72-year-old announced the delay in a statement on social media.
"I've been enjoying my time at home with the family while the world navigates its way through the Covid-19 pandemic. But, I really miss being on the road and performing for my beloved fans in my Farewell Yellow Brick Road Tour.
"While the scientists are making great progress, we are making big plans for a return to touring that will allow us to ensure the health and safety of everyone."
Sir Elton said delays to the European and North American tours had caused the further delay to the New Zealand dates.
"Don't worry about me. I'm using my downtime to keep myself fighting fit and healthier than ever. I'm raring to go!
"As always, thank you so much for your loyal support. I look forward to seeing all you wonderful Elton John fans soon. In the meantime, please stay safe and be well. Thank you."
The music legend was forced to cut some of his February concerts short, leaving the stage about two thirds of the way through his concert at Mt Smart in Auckland after contracting "walking pneumonia" and losing his voice.
He broke down in tears when he realised he couldn't complete his set.
"I'm sorry, so very sorry," he told the Mt Smart crowd.
The superstar, who earlier needed medical assistance while on stage, had to be assisted from the stage after attempting to launch into Daniel, but having no voice left.
The song was number 16 in a 25-strong playlist. NZ Herald concert reviewer Karl Puschmann said John's voice remained powerful during his early songs - until he spoke.
Sir Elton later reached out to fans on social media saying he was "disappointed and deeply upset" that he couldn't complete his show.
On February 4, he played to a packed Forsyth Barr Stadium in Dunedin in a show lasting more than two hours and with no incidents.
