Industrial production in Europe's biggest economy rose by a better-than-expected 1.6 percent in January over the previous month, driven by increased activity in all sectors, the economy ministry said in a statement.
In December, output had dropped by 2.6 percent month-on-month.
"Industrial output started the year with a perceptible increase, with impulses coming from both the manufacturing and the construction sectors," the ministry said.
Output in the manufacturing sector increased by 1.4 percent month-on-month, energy output was up 1.7 percent and construction output powered ahead by 4.3 percent, the data showed.
But the ministry remained cautious regarding the outlook for the next few months.
"In view of a current lull in orders, output is likely to remain subdued for now, but brighter sentiment indicators suggest the current weakness will be overcome," it said.
Data released on Wednesday showed that industrial orders in Germany fell sharply in January, wiping out the modest increase the previous month as export orders slumped.
UniCredit economist Andreas Rees said the industrial production data were likely to remain volatile.
Construction output, for example, which had benefitted from the mild weather in January, would likely have plunged again in February in view of freezing cold weather.
Nevertheless, while "the recovery path in hard data might be bumpy, it is a recovery," he said, arguing that forward-looking indicators "heralded better times ahead."
ING Belgium economist Carsten Brzeski said the output data provided "first evidence of a tender rebound of the German economy."
The February freeze "will probably also take a toll on the construction sector," he cautioned. But "once that is behind us, there are still enough reasons to expect a rebound of the German economy."
Commerzbank economist Ralph Solveen also believed "the trend will remain up in the coming months and the German economy will thus achieve a small increase in gross domestic product in the first quarter."