Output increased by 1.2 percent month-on-month, preliminary Economy and Labour Ministry data showed on Monday, beating economists forecasts for a rise of 0.9 percent from August.
The September output gain was led by a 1.4 percent increase in manufacturing output, which helped total production to rise by 1.3 percent in the third quarter from the April-June period, the biggest quarterly jump since the final quarter of 2003.
In a statement, the ministry said that with orders strong and German firms apparently coping well with high oil prices, coming months should also see a further increase in output.
Postbank economist Fabienne Riefer said the data showed Germany's manufacturing sector was in good health, and forecast the economy had grown by 0.4 percent in the third quarter after it stagnated in the April-June period of this year.
"In the light of today's data, we see a clear upwards risk to the (third quarter) forecast," she wrote in a research note.
The Federal Statistics Office is due to issue an estimate for German third quarter GDP at 0700 GMT on November 15.
Dekabank economist Andreas Scheuerle said he expected GDP growth to remain robust until the first quarter of next year, but noted that Germany still depended heavily on exports to power growth due to a persistent weakness in domestic demand.
Retail sales fell by almost one percent in the three months up to September from the second quarter, dogged by nagging concerns about high unemployment, which has eased, but is still close to five million.
The retail gloom is likely to be exacerbated next year, if, as has been strongly mooted, the country's two main political parties agree to raise value added tax.
A breakdown of the output data showed that energy production increased by 0.7 percent, whereas the recession-mired construction sector saw output dip by 2.5 percent.
The rise in production in September mirrored a gain in the Ifo research institute's measure of business confidence during September - a trend which accelerated substantially in October.
The monthly survey of purchasing managers (PMI) in German manufacturing also showed a strong pick-up in October.
The output data follow a fourth strong rise in manufacturing orders in the last five months in September, fuelling the strongest quarterly rise in orders in over five years.