With trade spats, cooling global demand and geopolitical crises all coalescing to hit growth, the world economy is heading for its weakest expansion since the financial crisis.
Other figures showed there had been a 1.5% fall in industrial output in May.
The German government already announced in April that it would lower the growth forecast for the year.
While fears of a chaotic Brexit are helping to drag down the German economy, global trade conflicts and troubles in the auto industry have been mainly blamed for the weak performance of the largest member of the 19-country euro currency union.
Signs for the next quarter look "ominous", Capital Economics said in an email.
In a statement to the populist tabloid Bild, Economy Minister Peter Altmaier said Wednesday's data was a wake-up call, calling for a more expansionary budget.
A spokeswoman said, "As the chancellor has already laid out, the government does not now see any need for further measures to stabilise the economy, the fiscal policy of the German government is already expansive".
Figures due out today could show the German economy shrank in the second quarter of this year.
Construction itself fell after an unusually good first three months, boosted by a mild winter.
"The risk of a recession is now elevated, but indicators for domestic private demand remain relatively resilient, especially in the services sector and with respect to consumers' spending".
Germany was not alone in seeing sharp moves in its bond market, as 10-year United States treasury yields dropped eight basis points to 1.62pc, and dipped below 1.63pc on two-year paper for the first time ever.
But UniCredit analyst Andreas Rees suggested the positive effect of those factors was limited. Here are the four key problems facing the stumbling German economy as it nears recession.
ING's Brzeski said a national debate about easing fiscal policy to provide stimulus - a focus for worldwide criticism of the government's economic management since the peak of the financial crisis - would get more heated.
In an article by BDI's managing director Joachim Lang published on Wednesday by the business daily Handelsblatt, it is argued that the balanced budget policy "should be called into question in an economically fragile situation".
The German government had a fiscal surplus of €58bn (£53.6bn) in 2018, so it has plenty of cash to spend, should it choose.