The euro was down 0.3 percent at 142.01 yen.
The euro zone Composite Purchasing Managers Index, which gauges how thousands of manufacturing and services companies fare every month, rose to 52.1 in December, in line with forecasts, with readings above 50 indicating growth.
The euro was last year's best-performing major currency—driven by factors such as euro zone banks repatriating funds to shore up their capital bases and repaying cheap loans to the ECB—but it lost ground late last week.
The upbeat euro zone data came ahead of he ECB's first policy meeting of 2014 on Thursday. While another rate cut after November's surprise move is seen an unlikely, the bank has the ability to issue further cheap loans to banks.
Investors are looking to minutes of the U.S. Federal Reserve's December meeting, due on Wednesday, for signs of how trading in the early part of the year will unfold. The minutes could hint at the timing and pace of any further reductions in Fed stimulus.
(Read more: Ding ding: Taper tantrum round two?)
Friday will bring the December U.S. payrolls report, which could suggest whether domestic job growth is strong enough for the Fed to continue tapering its asset buying.
The yen, meanwhile, pulled away from recent five-year lows versus the dollar and the euro as a fall in global stocks prompted traders to buy the safe-haven Japanese currency.
Asian shares led global stocks lower after growth in China's services sector slowed sharply last month.
The Nikkei and the yen—last year's weakest major currency—tend to move in opposite directions.
The dollar was last down 0.6 percent to 104.17 yen, according to Reuters data.