Markit's final Manufacturing Purchasing Managers' Index (PMI) for the euro zone fell to 50.3 in September from August's 50.7 and lower than earlier estimates of 50.5.
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The figure marks a 14-month low for the region, as input costs and selling prices were both lower than in previous months.
"September's euro zone PMI makes for gloomy reading. The euro area's manufacturing economy has lost the growth momentum seen earlier in the year, lurching closer to stagnation," said chief economist at Markit, Chris Williamson.
"The near-term outlook also looks worrying. Order books are now deteriorating for the first time since June of last year, suggesting output could start to fall as we move into the final quarter of the year," he said.
Along with Germany, Greece's factory activity contracted at the fastest rate in almost a year with Markit's PMI reading for the country coming in at 48.4, down from 50.1 in August.
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Ireland remained on top of the national PMI league table for the seventh straight month in September, despite seeing its rate of growth ease from August's near 15-year high, followed by Spain.
"In a sign of spreading economic malaise, Germany, Austria and Greece all joined France in reporting manufacturing downturns in September," Williamson added.