The rate of UK Consumer Prices Index inflation fell to 0% in June, from 0.1% in May, official figures show.
Falls in clothing and food prices were the main contributors to the change in the rate, the Office for National Statistics (ONS) said.
The ONS said the rate was also affected by a smaller rise in air fares in June than a year ago.
Bank of England governor Mark Carney has said he expects inflation to remain low in the immediate short term.
But the Bank expects it to start picking up around the turn of the year.
The rate of Retail Price Index (RPI) inflation – which includes housing costs such as mortgage interest payments and council tax – was 1% in June, unchanged from May.