The Markit Eurozone Purchasing Managers' Index for the eurozone dropped from 47.3 in February to 46.6 in March in a flash estimate, which is subject to revision.
The region's PMI has been less than 50, which indicates a contraction, for 20 consecutive months, Markit said.
Various component indexes are also on long losing streaks. The index for business output, at 46.5, has been negative for 14 consecutive months, hitting a four-month low in March. The new orders index is in the red for the third consecutive month and the employment index turned in its 15th consecutive month of contraction in March.
Manufacturing in the eurozone "deteriorated at a quickening rate in March," Markit Chief Economist Chris Williamson said in a statement.
"Instead of the eurozone economy stabilising in the second quarter, as many -- including the European Central Bank -- have been hoping to see, the downturn could therefore intensify in coming months."