Fruit and vegetable prices rose 4.9 per cent, the largest contributor to the monthly rise.
The monthly rate of food price inflation was higher than the previous rise between April and May, which was 0.7 per cent.
"We typically see price rises for many vegetables in winter due to seasonal effects," Smillie said.
"The vegetables that are most influencing this increase are tomatoes, cucumbers, and green beans. Whilst cucumbers and green beans have both reached their highest recent June prices, tomatoes have bucked that trend and fallen 30 per cent in June 2022 compared with June 2021."
Food prices have been in the spotlight lately amid a market study into New Zealand's supermarket sector.
The study, released by competition watchdog Commerce Commission, revealed the extent of the duopoly in the supermarket sector - led by giants Countdown and Foodstuffs.
The Commission estimated Countdown and Foodstuffs were making excess profits of about $430 million a year - more than $1m a day.
In response, the Government put the duopoly on notice, warning the sector to change "at pace" or face regulation.
A new Grocery Commissioner was announced last week, to be based within the Commerce Commission, to hold the sector to account and ramp up competition.
The Commerce Commission will get about $4.8 million of Government funding to make this happen.
Commenting on the latest figures, Foodstuffs managing director Chris Quin said the co-operative's stores had kept price increases for customers below inflation for the last two months.
Foodstuffs' 460 members own and operate individual stores under the New World, Pak'nSave, and Four Square brands around New Zealand.
Quin said global and domestic challenges had pushed up the costs of growing, making and retailing groceries. International freight costs had also risen significantly in the last six months, he said, adding that the standard cost to Foodstuffs in this area had risen from between $500,000-$1m to $2-3m per month.
"We've seen fuel related price increases for freight adjusted upwards again in June to now sit at over 26 per cent this year. Global supply chain issues, currency changes, skills shortages and increases in the price of equipment and ingredients are still flowing through to price increases with suppliers seeking to recoup higher costs on key inputs such as wheat, sugar, edible oils and meat. Though we have seen less price increases from suppliers in the last month than in May, the average cost price increase on these remains high.
"The rest of 2022 will remain challenging for New Zealand households caught in the middle of inflation pushing many prices up and mortgages going up to push inflation down," Quin said.