Industrial output fell by 1.2 percent on the month, the strongest decline since August 2014, data from the Economy Ministry showed. The figure fell short of the consensus forecast in a Reuters poll for a 0.4 percent increase.
"Industrial production went through a dry spell at the end of 2015," the economy ministry said in a statement, adding, however, that a rise in industrial orders in the fourth quarter pointed to an expansion in production at the start of this year.
Separate data from the Federal Statistics Office showed that seasonally-adjusted exports fell by 1.6 percent in December while imports were also down by 1.6 percent, narrowing the trade surplus to 18.8 billion euros.
Economists polled by Reuters had expected exports to rise by 0.5 percent and imports to go down by 0.5 percent.
"German industrial production dropped by a depressing 1.2 percent month-on-month in December, putting an end to a rather disappointing year for the German industry. This was the sharpest monthly drop since August 2014," ING-DiBa chief economist Carsten Brzeski said in a note.
For 2015, Germany registered a new record trade surplus of 247.8 billion euros, up from 213.6 billion euros in 2014, the data showed.