Europe's largest economy grew by 0.2% between July and September, half the 0.4% rate seen in the previous three months.
This was slower than economists had expected and well below the 0.7% rate recorded in the first quarter.
"The development of foreign trade had a downward effect on growth," said Germany's Federal Statistics Office.
"Exports were slightly down while imports were slightly up compared with the second quarter of 2016.
"Positive impulses on the quarter came mainly from domestic demand," the statistics body added. "Both household and state spending managed to increase further."
Some analysts said that the uncertainty caused by Britain's vote to leave the European Union may have counteracted solid domestic activity.
"Brexit meets solid domestic economy. This is probably the best description of the German economic performance during the third quarter," ING Bank economist Carsten Brzeski told Reuters.
He added that there was a threat to the economy from Donald Trump's US election victory if he followed through with campaign pledges to limit foreign imports.
"If Germany's single most important trading partner, the US, really moves towards more protectionism, this would definitely leave its mark on German growth."
Signs of slowing economies also emerged in other European countries, with GDP growth coming in below forecast for Norway, the Czech Republic, Slovakia and Hungary.
Italy bucked the trend, however, reporting slightly faster-than-expected growth of 0.3% in the third quarter, after having stagnated in the second quarter.
The slowdown in Germany's growth rate means the country grew more slowly than the eurozone as a whole in the third quarter, with the 19-nation bloc expanding at a rate of 0.3%, according to latest estimates.
Howard Archer, chief European and UK economist at IHS Global Insight, said he expected eurozone GDP growth to pick up to 0.4% in the fourth quarter, given recent upbeat survey data.
He predicted the eurozone would grow by 1.6% in 2016 as a while, but thought growth could slow to 1.3% next year "as it is likely to be increasingly hampered by political uncertainties".
"The political environment could be increasingly problematic for eurozone growth over the coming months, especially given that the UK's Brexit vote in June and November's election of Donald Trump as US President fuels concern over potential political shocks in the eurozone," Mr Archer said.
"General elections are due 2017 in the Netherlands (in March), France (in April/May) and Germany (around September), and the Renzi government is looking vulnerable in Italy, particularly over constitutional reform."

Emergency services were called to New Road, Woodmancote, at 17:45 BST following reports of the accident
A police spokesman said an off-duty nurse and paramedics tried to save the woman, who was the driver of the car, but she was declared dead at the scene.
The van driver, a 53-year-old man from Cheltenham, was arrested on suspicion of drink driving.
Police are appealing for witnesses.
Germany's economic growth slowed in the third quarter of the year, dented by weaker exports, figures have shown.
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A woman died in a collision between a car and a van in Gloucestershire.