Seasonally-adjusted Gross Domestic Product also rose 0.2 percent in the full 28 member European Union, compared to 0.5 percent in the three months to March, Eurostat said.
Analysts had warned that the uptick in eurozone growth would not last.
The number of employed people meanwhile increased by 0.2 percent in both the eurozone and the bloc, compared to 0.4 percent in the first quarter, the EU statistics office said.
In June, seasonally adjusted industrial production fell by 1.6 percent in the euro area and by 1.5 percent in the EU 28, compared with the previous month.
In June 2019, compared with June last year, industrial production fell by 2.6 percent in the eurozone zone and 1.9 percent in the EU 28, reflecting the wider slowdown in the economy.