Production declined 1.3 percent in the 17-member currency region and 1.6 percent in the larger European Union from May of last year, Eurostat said.
Since April, durable goods production dropped 2.3 percent in the eurozone and 2.1 percent in the EU.
Capital goods production fell 1.5 percent in the eurozone and 1.9 percent in the EU.
Energy production rose in he eurozone, up 0.1 percent, but fell 0.3 percent in the EU.
Industrial production fell in 13 nations, rose in nine and remained unchanged in Britain. Twenty-three of 27 nations were included in the report.
The sharpest declines were in Romania, Lithuania and Sweden, where production fell 10.7 percent, 6.3 percent and 3.8 percent, respectively.
The largest gains were in Portugal, Latvia and Estonia, with industrial production up 6.1 percent, 2.2 percent and 2 percent.