Data from the Federal Statistics Office showed seasonally-adjusted exports fell by 5.2% from July to €97.7bn (£71.8bn).
Imports fell 3.1% to €78.2bn, the biggest one month drop since November 2012.
Meanwhile, manufacturing turnover fell by 1.3% from July after sales to euro area countries declined.
The data follows sharp declines in industrial orders and output in August, suggesting that waning demand from abroad, particularly China and other emerging markets, may be leaving its mark on Germany.
"This is a strong fall, the kind you don't see every day," said Holger Sandte, chief European economist at Nordea. "Weakness in China, Brazil, Russia and other markets is having an impact."
Germany, the eurozone's biggest economy, has reported four quarters of growth in a row.
But as well as a slowdown in emerging economies, the diesel emissions scandal that has hit Volkswagen could have knock-on effects on the rest of the German economy.
The German carmaking industry accounts for a large chunk of exports - 17.9% of Germany's €1.1 trillion in exported goods last year.
German exports fell in August by their largest amount since the height of the global financial crisis in 2009, and imports were also down sharply.