The Economy Ministry calculated that industrial orders rose by 1.7 percent in December from November, after dropping by 4.9 percent the previous month.
"The increase was due to a strong increase of 4.3 percent in overseas demand," notably from non-eurozone countries, the ministry said in a statement.
Orders from the eurozone dropped by 6.8 percent, but orders from outside the single currency area jumped by 12.3 percent. Domestic orders, on the other hand, were down by 1.4 percent month-on-month, the ministry calculated.
Taking the fourth quarter as a whole, German industrial orders fell by 1.4 percent, the ministry said.
"The outlook for industrial output is therefore subdued. At the same time, the continued improvement in business confidence at the start of the year suggests that an end to the current phase of weakness is in sight," it said.
Last month, the widely-watched Ifo business climate index for the third month in a row.
Analysts cautioned that the monthly orders data are notoriously volatile.
"As such, we wouldn't read too much out of one-month swings," said Annalisa Piazza of Newedge Strategy.
"The German economy has certainly moderated in the fourth quarter, as demand from abroad was hit by the global slowdown but today's data seem to suggest that factory activity has not collapsed," she said.
"If anything, a slight pick-up is expected in the first quarter of this year, given the upswing in business confidence indicators."
Carsten Brzeski of the Dutch bank ING also believed the high volatility of the industrial orders data "actually masks a trend of stabilisation.
"It is too early to call this a rebound. However, there is at least still sufficient demand for goods 'made in Germany' to keep the industrial engine running in 2012," he said.
Thorsten Polleit of Barclays Capital Research similarly believed the orders data "appear to send a stabilisation signal."
And Christian Schulz, senior economist at Berenberg Bank, said the figures "in isolation do not point to an imminent growth rebound yet."
But taken together with improving confidence indicators, he noted that "signs of hope for a swift recovery led by exports to markets outside the eurozone continue."