The Consumer Price Index was up 3.3 per cent year - the market had forecast 2.7 per cent.
This was the biggest increase in nearly 10 years and was driven by higher prices for new housing and petrol, StatsNZ said.
"Previously, annual inflation had peaked at 5.3 percent in June 2011, impacted by a GST increase of 2.5 percentage points that came into effect in October 2010".
"Before this, annual inflation reached 5.1 percent in the September 2008 quarter, during the time of the global financial crisis".
The Consumer Price Index (CPI) is a measure that pulls together a weighted average of prices for a basket of consumer goods and services, such as transportation, food and medical care.
It doesn't include house price inflation - which for the past few years has run far hotter than most goods and services - but it does include building costs and rental costs.
The spike takes annual inflation outside the Reserve BAnk's 1-3 per cent target range and is likely to put more upward pressure on interest rates.
Banks started lifting mortgage rates this week.
Most economist now expect the Official Cash Rate will be lifted in August.
The cost of building a new house was the biggest contributor to both annual and quarterly inflation this quarter, up 7.4 percent for the year, and 4.6 percent for the quarter.
"Higher prices for building houses reflect both supply-chain problems and high demand," said StatsNZ's prices senior manager Aaron Beck.
"Several construction firms have told us that it is hard to get many of the materials they need to build a house, and that there are higher labour and administration costs.
"In addition, in the year to May 2021, $18.3 billion of residential building work was consented, up 18 percent on a year earlier."
