Immigration officials said Albert Buitenhuis, who weighs 130kg (286 pounds), did not have "an acceptable standard of health".
He now faces expulsion despite shedding 30kg since he moved to the city of Christchurch six years ago.
New Zealand has one of the highest obesity rates in the developed world, with nearly 30% of people overweight.
Mr Buitenhuis and his wife, Marthie, moved from South Africa to Christchurch in 2007. At the time, the chef weighed 160kg.
Until now, their annual work visas had been renewed with "very little problem", his wife said.
"We applied year after year and there were no issues," she said.
"They never mentioned Albert's weight or his health once and he was a lot heavier then."
But in early May, the couple was told their work visas had been declined because of Mr Buitenhuis's weight.
"The irony is that at the moment he weighs less than when we first arrived in New Zealand and also less than in his first medical, which was accepted by [immigration authorities]," his wife said.
The couple has appealed to New Zealand's immigration minister, citing the chef's recent weight loss.
An immigration spokesman said Mr Buitenhuis's application had been rejected because his obesity put him at "significant risk" of complications including diabetes, hypertension and heart disease.
"It is important that all migrants have an acceptable standard of health to minimise costs and demands on New Zealand's health services," he said.
http://www.bbc.co.uk/news/world-asia-23475583
