The monthly rise in Europe's top economy compared to February was far higher than the 1.8-percent rise in seasonally adjusted terms forecast by economists polled by Dow Jones Newswires.
In February, industrial production slipped 0.2 percent. The ministry attributed March's sharp rise largely to the end of the bitterly cold winter, which gave the construction industry in particular a strong boost.
"With it, the recovery in industrial output continues, for the first quarter as a whole as well," the ministry said in a statement. "In light of the robust upturn in domestic and foreign demand for industrial output, it should continue in the coming months."
Jennifer McKeown, senior European economist at Capital Economics in London, said the fresh data were encouraging but warned that the economic revival might be more tentative than hoped.
"Note that in (the first quarter) overall, German industrial production rose at a similar rate to that seen in (the fourth quarter), suggesting that the overall economic recovery might not have resumed," he said.
"And while growth should pick up in (the second quarter) and beyond, there is still no sign of the consumer revival that would be needed to sustain a strong recovery in Germany or boost demand for other countries' exports."
The Economy Ministry on Thursday announced that demand for German manufactured goods soared 5.0 percent in March driven by both domestic demand and exports, in a further glimmer of economic recovery.
After suffering its worst post-war recession, with the economy contracting by five percent last year, the German government has forecast growth of 1.4 percent in 2010.