The data released by the Economy Ministry was far better than expected by economists polled by Dow Jones Newswires who had forecast a rise of just 1.0 percent following flat figures in February compared to the previous month. The ministry said the growth was seen across a "broad front."
"That indicates a continuation and consolidation of the recovery process for industrial production," it said in a statement.
"Business confidence indicators, which also recently improved, also point in this direction."
The closely watched Ifo index last month showed business confidence in Germany rising sharply to a near two-year high. However retail data released Tuesday showing a 2.4-percent plunge in March raised fears that German gross domestic product had contracted in the first quarter of the year.
The data released Thursday said foreign demand for industrial products in Germany, the world's second largest exporter after China, rose 4.7 percent in March, with even stronger growth in orders at home of 5.4 percent.
Orders from the other 15 countries in the eurozone rose 9.6 percent in March from February, while orders from beyond the currency bloc gained 1.3 percent.
Economist Alexander Koch from UniCredit Group said Europe could take heart in the data.
"The latest jump in orders from the EMU neighbour countries, which still account for the bulk of German exports, confirm that, despite the Greek debt crisis and the feared contagion to other member countries, the revival in global industrial activity remains broad based," he said.
Demand for consumer goods, however, was weak, falling 1.9 percent in keeping with a long-term trend. Berlin has faced pressure from eurozone trade partners for policies that would boost imports from neighbours.
Analyst Carsten Brzeski of ING Bank said the figures marked an "impressive comeback."
"After the weather-driven temporary dip at the turn of the year, at least the German manufacturing sector has picked up speed again," he said in a statement.
"Whether the pick-up came just in time to prevent another quarter of negative growth will only become clear next week with the first GDP estimate to be released."
Brzeski said he would also be looking to the release of March data on industrial production Friday to indicate whether Germany's economic "hibernation" had ended.