The German composite PMI rose to 54.0 from 53.7 in August, moving further above the 50 mark, which denotes growth.
The corresponding survey for the euro zone, however, showed business activity expanding at a slightly weaker pace than expected as companies cut prices for the 30th month in a row.
Overall, the data did little to alter the picture of a sluggish recovery in the euro zone.
The euro's rise stung the dollar index, which shed 0.33 percent. The index last traded at 84.472, having peaked at 84.861 on Monday, a high not seen since July 2010.
The basket of six currencies traded against the dollar had posted 10 straight weeks of gains through Friday as markets wagered U.S. rates would rise long before those in Europe or Japan.
The dollar's run even prompted New York Federal Reserve Bank President William Dudley to caution that the gains could complicate the Fed's job, potentially hurting U.S. economic performance and pushing down inflation.
Dudley said on Monday that while the value of the dollar was not a policy goal of the Fed's, it had to be taken into account as part of the central bank's economic forecast.
The dollar also eased 0.2 percent to 108.62 yen, down from a six-year high of 109.46 set on Friday.
There was not much boost for either the Japanese currency or its safe-haven peer, the Swiss franc, to news that the United States and partner nations had carried out the first air strikes against Islamic State in Syria, opening a new front in the battle against militants.
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