The June figure was the lowest since the same month the year before, when consumer prices rose 0.08 percent, the Brazilian Geography and Statistics Institute (IBGE) reported.
Markets had expected consumer prices to edge up 0.3 percent in June as they did in May.
Food products and drinks, which rose the most in previous months, showed increases of only 0.04 percent, unlike transport which surged 0.14 percent last month when the country was jolted by mass street protests over public transport fare hikes, inadequate funding of health and education and endemic political corruption.
From January to June, accumulated inflation reached 3.15 percent.
In May, 12-month inflation reached 6.5 percent, the upper limit of the official target, sparking public alarm and a drop in President Dilma Rousseff's approval rating that was reflected in polls conducted in early June
The Central Bank recently raised its inflation forecast for 2013 to six percent.
Last year, consumer prices rose 5.8 percent after a hike of 6.5 percent in 2011.
The country's GDP meanwhile grew by a paltry 0.9 percent in 2012, down from 2.7 percent the previous year.