Exports rose 0.9 percent during the month, following a 1.5 percent increase in February, the Federal Statistics Office in Wiesbaden said. Economists polled by Bloomberg had forecast a 0.5 percent decline.
At the same time, March imports rose 1.2 percent, faster than the 1 percent gain forecast by economists.
Wednesday's data confirmed that sales at German businesses were booming in markets outside the European Union, where they recorded growth of 6.1 percent, compared to the year-earlier result. Meanwhile, exports to countries in the crisis-hit region shrank by 3.6 percent.
The value of German exports hit €98.9 billion ($128.4 billion) in March, and imports reached €81.5 billion.
These were the highest monthly figures ever recorded for exports and imports (both previous all-time highs recorded in March 2011), the statistics office said.
Driven by the unexpected rise in exports, Germany's foreign trade surplus widened to €17.4 billion in March from €14.9 billion in the previous month, and well above the €14.3 billion consensus estimate.
Separate reports showed that factory orders and industrial production both rose more than economists forecast in March.
Industrial output jumped 2.8 percent from February, when it fell 0.3 percent, Economics Ministry data showed Tuesday. That's the sharpest increase in eight months and far stronger than the consensus forecast of a 0.8 percent rise.
Meanwhile, factory orders gained 2.2 percent, a Monday report showed.
The German economy contracted by 0.2 percent in the fourth quarter of 2011. The International Monetary Fund forecasts the region's economy will contract 0.3 percent this year.
Official figures for Germany's first-quarter gross domestic product are due on May 15.
Germany's benchmark DAX share index fell 25.98 points, or 0.40 percent, to trade at 6,418.76 on Wednesday.