The expansion was the highest since July 2011, with cold weather boosting energy use and adding to the jump in production.
Strong German and Dutch factory figures led the rise across most countries, though France and Italy failed to grow in the month.
The positive figures set the tone for a strong day on Europe’s stock markets – Germany’s Dax increased 0.72 per cent and the Eurostoxx 50 rose 0.66 per cent.
Germany’s ZEW survey of market sentiment was largely unchanged, rising 0.1 per cent from 36.3 points to 36.4 points this month. Expectations are still significantly down from 48.5 points in March, following a big decline in April.
“This may be due to the still poor economic situation in the Eurozone, that is also reflected by the recent ECB interest rate cut,” according to ZEW president Professor Clemens Fuest.
And analysts at Capital Economics warned investors not to expect a widespread recovery yet.
“There are few signs the rest of the economy has seen any meaningful recovery,” said Ben May. “We expect Eurozone GDP to have contracted by 0.2 per cent in the first quarter.”