According to regular data compiled by the economy ministry, industrial output fell by 1.2 per cent in December, disappointing analysts' expectations for a modest increase.
Factory output - a key yardstick for gauging the health of Europe's biggest economy - had already declined fractionally by 0.1 per cent in November.
In December, it was weighed down by falling activity in all main sectors, with manufacturing output down by 1.1 per cent month-on-month, energy output contracting by 3.0 per cent and construction output slipping by just 0.2 per cent, the ministry said.
Separately, the federal statistics office Destatis said that both exports and imports declined in December.
In calendar- and seasonally-adjusted terms, exports fell by 1.6 per cent to 97.8 billion euros (USD 109 billion) in December and imports also declined by 1.6 per cent to 78.4 billion euros.
That caused Germany's trade surplus - the balance between exports and imports and a key gauge of an economy's comparative strength - to contract to 19.4 billion euros, Destatis calculated.
Nevertheless, taking 2015 as a whole, Germany clocked up its highest-ever trade surplus as both exports and imports powered ahead to new annual records.
The industrial output data "was the sharpest monthly drop since August 2014," said ING DiBa economist Carsten Brzeski.
While the decline could be partially explained by the timing of the Christmas holidays, taking the fourth quarter of last year, industrial production was down almost one per cent, "illustrating the general weakness of Germany's former growth engine," Brzeski said.
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