Markit's Eurozone Flash Services Purchasing Managers' Index, made up of surveys of around 2,000 businesses ranging from banks to restaurants, slumped to 53.6 in September from 55.9 in August, its lowest reading since February.
The index has now been above the 50.0 mark that divides growth in business activity from contraction for just over a year but was well below the consensus forecast in a Reuters poll for 55.5.
"Quite a dramatic easing since September, but the third quarter as whole is not looking too bad. It's still a strong pace of growth ... we think we are looking at (GDP) growth in the region of 0.6 per cent," said Chris Williamson at data provider Markit.
The pace of growth in the euro zone manufacturing sector, which drove a large part of the economy's return to growth in the third quarter of last year, saw its pace of growth ease off to its slowest since January.
The flash manufacturing index fell to 53.6 in September from 55.1 in August, missing forecasts for 54.5, while the output index sank to 54.4 this month, from 57.1 in August.
The composite index, made up from the services and manufacturing sectors and often used to predict overall growth, sank to 53.8 this month from 56.2 in August, well short of expectations for 55.7.
The euro zone escaped from its deepest recession in post-war history in the third quarter of last year, having pumped billions of euros into recovery measures, and relatively strong second-quarter growth of 1.0 per cent announced last month surprised markets.
Still, economists in a Reuters poll expect economic growth to slow to a crawl over coming quarters as austerity packages begin to bite, though the chances of the bloc slipping back into recession remain slim.
Median forecasts from the poll of around 70 economists predict the 16-nation bloc will grow by 0.2 to 0.4 per cent each quarter through to the end of next year.
The manufacturers' new orders index slumped from 55.3 in August to 52.8 in September, its lowest in a year, on the back of a slowdown in global trade in recent months.
The service sector saw its new business index fall by a similar margin.
Data released on Wednesday showed industrial new orders fell more than twice as much as expected month-on-month in July, pulled down by a slump in demand for capital and durable consumer goods.
However, service sector's business expectations index – which gives an indication of how firms think the situation will be in a year's time – rose to 68.1 this month from August's 67.1, its highest reading since April.