Business weakness will complicate the European Central Bank's efforts to ready markets for a rate hike in July.
The RBS/Markit Eurozone Purchasing Managers Index for services companies, which range from cafes to banks, fell to 49.5 in June from 50.6 in May, the first time it has sunk below the 50.0 mark dividing growth from contraction since June 2003.
Only three of 36 economists had forecast a move below 50.0, with the lowest prediction being 49.7 and the median 50.5.
Euro zone manufacturing also suffered a bruising month. The RBS/Markit Eurozone PMI for the sector fell to 49.1 from 50.6, its lowest level since May 2005 as new orders slipped further. Economists had forecast a dip to 50.2.
Meanwhile, German business morale fell more than forecast in June to its lowest level since December 2005 with the Ifo index at 101.3 from 103.5 in May.
The euro hit session lows after the data to around $1.5501 to the dollar from $1.5559, while bund futures also rallied to session highs.
"The falls are probably not sharp enough to stop the ECB hiking in July ... But the data today will cause some intense debate about rate-setting," said Juergen Michels at Citi.
Earlier Flash data showed French growth in both manufacturing and services contracted in June, but remained above the 50.0 level in Germany.
The data showed inflation putting services companies under intense pressure as their input costs rose at the fastest pace since September 2000.
ECB Executive Board member Lorenzo Bini Smaghi said on Friday the bank would have to raise rates unless services sector productivity picks up to counter higher commodity prices.
Although companies responded to higher costs by raising their charges in June at the steepest rate since November 2000, they lagged the rate of cost increase by the widest margin since November 2004.
And the service sector's optimism about future business is waning sharply.
The business expectations index eased to 54.9 in June, its lowest level since the survey began in 1998, and lower even than after the attacks on the United States in September 2001.
Falls in the services and manufacturing PMIs took the Composite index down to 49.5, its lowest since June 2003.