Industrial orders dropped by 2.4 percent in November compared with the previous month, the economy ministry said in a statement.
In October, German factory orders had risen by 2.9 percent.
Domestic orders slumped by 4.7 percent and export orders slipped by 0.7 percent compared with the previous month.
Orders from the eurozone rose by 2.7 percent while those from outside the eurozone were down by 2.6 percent, the ministry calculated.
By sector, orders for semi-finished goods fell by 2.3 percent and those for capital goods slumped by 3.1 percent, while demand for consumer goods rose by 2.6 percent.
Analysts said the surprisingly steep drop in the headline number was no cause for outright concern.
"It was the first decline after two consecutive and strong increases.
Hence, there is no need for being disappointed," said UniCredit economist Andreas Rees.
"We have to be a bit more patient. In terms of business sentiment, there is more and more evidence that German companies already turned the corner.
However, hard data typically lag behind such leading indicators. While economic momentum should have remained subdued at year-end 2014, an acceleration in the first quarter of 2015 is in the pipeline," Rees said.
Commerzbank economist Marco Wagner agreed, noting that the strong increase in orders the previous month had been distorted upward by big-ticket orders for vehicles and aircraft.
"In all, orders in October and November were around 0.5 percent higher than in the third quarter, a positive signal suggesting that the German industry has overcome its soft patch," Wagner said.
BayernLB economist Stefan Kipar said the weaker euro and falling oil prices "should provide a boost to the global economy in 2015. And the internationally competitive German industry should benefit from that."
Natixis economist Johannes Gareis was confident that the German economy would not "fall back into recession in the fourth quarter."
Berenberg Bank economist Christian Schulz calculated that factory orders "remained on a moderate uptrend in the fourth quarter, despite the sharp drop in November."
The data "add to the upside risk to our fourth-quarter forecast for German growth," he said.