They eventually identified 58 children who had been affected.
Study co-author Dr Ben Wheeler said they pin-pointed the key risk factors for the disorder as having darker skin pigment, Indian and African ethnicity, being under three years old, exclusively breastfed, and living in the far South, particularly during winter and spring.
Specifically, the median age was 1.4 years, 47 per cent were male and 95 per cent of the children were born in New Zealand while the majority of the mothers - 68 per cent - were born outside this country.
Overall, the annual incidence of rickets in children aged 15 years and under was just over two in every 100,000, and 10.5 in every 100,000 among those aged under three.
The most common features among those affected were skeletal abnormalities, poor growth and motor delay.
"While we found the highest population rates of Vitamin D deficiency rickets in children living in Otago and Southland, nearly a third of all cases were reported in Auckland and Northland," he said.
"Of the 58 patients identified, we found none had previously received appropriate Vitamin D supplementation, which is concerning."
In their article, published in the Australian and New Zealand Journal of Public Health, Dr Wheeler and his co-authors concluded that to reduce the incidence of the disease among those at risk, efforts should be focused on increasing awareness - and implementation - of existing policies for targeted maternal, infant, and child Vitamin D supplementation.
Dr Wheeler said there had been mounting concern worldwide that the number of children suffering from Vitamin D deficiency and Vitamin D deficiency rickets was increasing.
A study published in 2013 showed that in Britain, where rickets largely disappeared in the 1950s with mass programmes to give children cod liver oil, the disorder was on the rise, with the number of reported cases of rickets in hospitalised children increasing from 183 cases in 1995 to 762 cases in 2011.