Pregnant women with iron deficiency are more likely to go into premature labour or deliver a baby with low birth weight.
They are also more likely to be iron deficient while they are breastfeeding.
The study analysed cord blood samples from 131 children and mums were interviewed.
"Although the sample of children we tested was quite small, they are broadly generalisable to all children born in New Zealand today, and the results give us a good indication of iron deficiency as an issue," Dr Grant said.
He recommends pregnant women who drink large amounts of milk each day take iron supplements.
"An alternative would be to increase the nutrient content of milk consumed by mothers-to-be to keep both the mother and child healthy."
Iron deficiency is the most common micro-nutrient deficiency worldwide, with pregnant women and children under five most at risk.
Iron is essential for healthy brain development, and a lack of the nutrient in babies and toddlers, when the brain is developing rapidly, is associated with subsequent small differences in brain function and in child behaviour and learning.