The European Commission's spring forecast confirmed its prediction of a 0.3% contraction in 2012 in the economies of the 17 countries that use the euro.
It predicted growth of 1.0% for the eurozone in 2013.
European Commissioner for Economic and Monetary Affairs Olli Rehn said "a recovery is in sight" for the eurozone.
But he added: "The economic situation remains fragile, with still large disparities across member states."
For all 27 countries in the EU, the Commission is predicting zero growth for 2012, with 1.3% growth next year.
Growth figures for the first quarter of 2012 will be released by the European statistics agency Eurostat on Tuesday 15 May.
"Economic activity in the EU contracted in the last quarter of 2011 and is estimated to have also done so in the first quarter of 2012," the Commission said in its statement.