Greece was the worst affected country, with 59.1% of under-25s unemployed. This is followed by Spain at 55.9% and Italy at 38.4%.
Eurostat figures revealed unemployment in the 17 countries hit 12.1% in March, up from 12% in February - equivalent to 19.2 million jobseekers.
Greece and Spain recorded the highest overall unemployment rates in the eurozone, at 27.2% and 26.7% respectively, while Austria, at 4.7%, and Germany, at 5.4%, had the lowest rates.
The EU's employment and social affairs commissioner Laszlo Andor warned EU institutions and governments, business and social partners at all levels need to do all they can to avoid a "lost generation".
There was better news in the UK, as the latest job index from recruitment site Reed revealed the jobs market grew slightly in April, with year-on-year growth remaining strong.
The April figures follow a strong first quarter for the UK jobs market, with 9% more job opportunities on offer during the first three months of the year, compared with the final quarter of 2012.
This rise echoes the recently announced GDP figures, which showed the UK economy grew by 0.3% in the first three months of the year.
A significant majority of sectors (85%) are now stronger than they were this time last year, with particularly strong gains in social care (64%), construction (60%), education (51%) and health and medicine (51%).
Chairman of Reed James Reed said: "We're now seeing people apply for new jobs in unprecedented numbers, as many who have been sitting tight during the tough economic conditions of the last few years gain the confidence to look at furthering their careers with a new employer.
"Salaries have remained static for over three years against a rising cost of living, so now is the time for many people to look for something new."
