This paper focuses on the impact of economic policy uncertainty on risk spillovers within the Eurozone and contributes to these two growing literatures. To this end, we adapt the two-step procedure developed by Adrian and Brunnermeier (forthcoming) in the framework of financial systemic risk to the sovereign bond market. Accordingly, we attempt (i) to measure the extent to which distress affecting one given country's sovereign spreads can affect the Eurozone's bond market as a whole and then (ii) to identify the determinants of risk spillovers by estimating a panel data model with macroeconomic state variables and economic policy uncertainty (EPU) indices introduced by Baker et al. (2013) as regressors. EPU indices considered concern the four largest Eurozone countries, i.e. Germany, France, Italy and Spain, as well as the United States. The model is estimated with quarterly data for ten countries representing the bulk of debt issuances within the Eurozone over a period ranging from Q4/2008 to Q2/2013, which is characterized by historically high dispersion of sovereign bond spreads either across time or across countries. Our results support the idea that economic policy uncertainty in the core economies of the Eurozone, i.e. Germany and France, as well as in the largest periphery countries, i.e. Italy and Spain, can create an environment likely to exacerbate the transmission of risk arising from abnormal developments of individual countries' sovereign spreads to the Eurozone bond market as a whole. In this respect, our results plead for larger effort of Eurozone "leaders" to reduce the uncertainty surrounding their economic policy in periods of crisis not only to avoid adverse effects on their own economies but also to reduce the risk of a destabilization of the Eurozone sovereign bond market as a whole.