The German economy ministry calculated that factory output contracted by 0.3 per cent in November compared with a month earlier, corrected for seasonal factors.
The previous month, output had increased by 0.5 per cent.
Falling activity in the key manufacturing sector provided the main drag on the headline figure, with manufacturing output down by 0.8 per cent month-on-month, the ministry said.
By contrast, construction output increased by 1.6 per cent and energy output was up 2.5 per cent.
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Here, activity in the energy, water and extractive industries fell, while manufacturing production grew slightly in the European Union's second leading economy.
Economists said both sets of data fell short of projections.
"November's disappointingly weak German and French industrial production figures provided further evidence that the hard data on the eurozone economy is failing to live up to the more optimistic picture painted by the surveys," said Capital Economics economist Jessica Hinds.
German trade data also failed to live up to expectations, with exports edging up by a meagre 0.4 per cent and the trade surplus contracting, the federal statistics office Destatis calculated.
"Granted, the surveys suggest that annual production growth might pick up soon. But industrial production would have to rise by 1.5 per cent month-on-month in December if the fourth quarter is merely to match the third quarter. This dents hopes that German growth picked up" in the fourth quarter after the disappointing expansion of 0.3 per cent in the third quarter, she said.