This is the third increase in a row after plus 1.3 percent in May and plus 4.6 percent in April, as the Federal Statistical Office announced on Wednesday morning.
Economists surveyed by the Reuters news agency had only expected growth of 1.0 percent this time.
"Price increases can increase the nominal export volume without actually exporting more," warned the chief economist at VP Bank, Thomas Gitzel, against too much euphoria when interpreting the figures.
"Price-adjusted, there should be less left over from the increase in exports," said the chief economist at Hauck Aufhäuser Lampe Privatbank AG, Alexander Krüger.
"Foreign trade will remain an economic problem child for the time being."
Imports increased in June for the fifth month in a row, although the increase of 0.2 percent was significantly weaker than in the previous months.
The trade balance - exports minus imports - again showed a clear plus of 6.4 billion euros in June.
In May it was only 0.8 billion euros.
Most German exports went to the United States in June.
After calendar and seasonal adjustment, 6.2 percent more goods were exported there than in May, with US exports totaling 14.2 billion euros.
Exports to the People's Republic of China rose by 2.4 percent to 8.9 billion euros, those to Great Britain by 4.2 percent to 6.0 billion euros.
Goods worth 72.9 billion euros were exported to the member states of the European Union (EU), 3.9 percent more than in the previous month.
However, the mood among German exporters clouded over at the beginning of the second half of the year.
The export expectations determined by the Ifo Institute fell in July to minus 0.5 points from plus 3.4 points in June.
"The gas shortage weighs on the outlook for German exports," said the Ifo Institute.