The unemployment rate added just 0.1 percentage point compared with May, reaching 6.4 percent, seasonally-adjusted figures from the BA federal labour agency showed.
Before the pandemic reached Germany in March, the rate had hovered around 5.0 percent since late 2018 as the country basked in the end of a post-financial crisis boom.
In absolute terms, less representative of underlying trends but more closely followed in public debate, the number of people out of work rose by 40,000 month-on-month, to over 2.8 million.
That was almost 640,000 more than a year ago.
“The labour market remains under pressure due to the coronavirus pandemic” although “massive use of shorter hours schemes have stabilised” employment, BA chief Detlef Scheele said in a statement.
Germany's shorter hours scheme known as Kurzarbeit, in which the government tops up workers' wages when their shifts are pruned back, was credited with saving many jobs in 2008-09 and has been widely copied since.
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After a surge to 10.6 million in March and April combined, the number of new workers covered by shorter hours applications fell to 1.1 million in May and just 340,000 in June, BA said.
New data showed that payments actually flowed to 2.5 million workers in March and 6.8 million in April, the authority added.
“The numbers resorting to shorter hours were far higher than those at the time of the Great Recession” of 2008-09, the BA said.
The IMK think tank has forecast three million unemployed by the end of the year compared with 2.3 million on average in 2019.
If that prediction comes true, “one cannot speak of mass unemployment” resulting from the pandemic, weekly Die Zeit commented ahead of Wednesday's data release.
“It shouldn't be ruled out that in the end, Germany will – yet again – escape with only a black eye,” Zeit added.