Prices gained 0.3 percent from May in Europe's largest economy, with energy and food leading the way, Destatis said.
Those two sectors represent more than half of the annualized global price increase and corresponded to around 20 percent of all household spending, it added.
“It was the third time this year that the three percent threshold was reached,” a Destatis statement said.
The overall cost of fuels leapt by 61.9 percent on the year, with motor fuels gaining 15.0 percent. If energy was excluded, “the year-on-year rate of price increase would have been 1.9 percent,” the statement said.
General food prices jumped by 7.6 percent in June from the same month a year earlier, with dairy products showing a gain of 18.9 percent. The cost of breads and cereals rose by 9.1 percent, but fish and seafood rose by just 1.2 percent.
Prices for durable consumer goods fell meanwhile, with computer equipment down by 16.4 percent on the year and TV sets costing 18.9 percent less on average.
The cost of services rose by 1.6 percent, in large part owing to rents, which account for 20 percent of the total calculation, Destatis said. But it nonetheless pointed out that “the price trend for rents has remained below the level of the consumer price index for a considerable time and thus has had a dampening effect on inflation.”