Overall production fell 0.1 percent month-on-month, figures from federal statistics authority Destatis showed.
But the dip was caused by lower output from energy and construction firms, a breakdown of the data showed, while industry increased output by 0.6 percent, led by makers of capital goods and consumer goods.
“The economic situation in industry remains lively, and the continuing positive picture in industrial orders points to this development continuing,” the economy ministry in Berlin said in a statement.
“Weak January data are rather a sign for an extended vacation period after Christmas than a structural slowdown,” ING Diba bank economist Carsten Brzeski said.
“At least in the near term, prospects for German industry have never looked rosier,” he added, although “the risk for Germany is for real” from a looming transatlantic trade war.
US President Donald Trump on Thursday signed off a 10-percent tariff on aluminium imports and 25 percent on steel, blasting “an assault on our country” from “aggressive foreign trade practices”.
'Call for level-headedness'
Trump singled out Germany in the announcement, arguing that “many of the countries that treat us the worst on trade and the military are our allies” — referring both to Germany's massive trade surpluses and its failure to meet NATO defence spending targets.
A separate Destatis release Friday showed Germany's trade surplus — the amount its exports outweigh its imports — remained high in January, with a reading of €21.3 billion ($26.2 billion) adjusting for seasonal and calendar effects.
Over the full year 2017, Germany's trade surplus shrank slightly to €245 billion, figures released last month showed.
That was far from enough to soothe grumbles from Europe and Washington that Berlin is not doing enough to stoke domestic demand and boost imports.
A tit-for-tat transatlantic trade war could be especially bad news for Berlin.
“The EU may now take steps we wouldn't want… we call urgently for level-headedness,” head of the BGA German exporters' association Holger Bingmann told news agency DPA.
While Brussels has vowed to tax US motorcycles, whiskey, orange juice and jeans in retaliation for the steel and aluminium levies, Trump has threatened the EU with a hike in duties on car imports in response.
The car industry is Germany's largest, employing some 800,000 people.