Exports fell 2.1% compared with October, German's Federal Statistical Office reported, while imports rose 1.5%.
Meanwhile, factory production fell by 0.1% from October as energy production fell and construction activity decreased.
The latest news follows weak industrial order figures this week.
"Things are certainly not rosy," said Bankhaus Lampe economist Alexander Krueger. "The geopolitical situation, especially the Russia conflict and the related economic uncertainty, is limiting growth,"
On a seasonally adjusted basis, the country's trade surplus shrank to €17.7bn (£13.9bn) in November.
Germany exported goods worth around €95.8bn and imported goods valued at €78.0bn in the month.
In December, Germany's economic affairs ministry said the country's recovery was "progressing at a slow pace."
This is a disappointing batch of German data. It pours cold water on hopes that the Eurozone's traditional economic powerhouse will drag its neighbours out of the gloom in the near future.
The figures don't necessarily point to a renewed contraction in the German economy.  But they are consistent with no significant acceleration from the feeble 0.1% growth that Germany recorded in the third quarter of last year, following a contraction of the same magnitude in the previous three months.
There were also declines in French and Spanish industrial production, adding another layer of gloom to the picture.
These figures provide a little extra support to the view that the European Central Bank will embark soon on a major programme of quantitative easing - buying financial assets notably government debt with newly created money.
German exports and production fell in November compared with the previous month.