The public health measures implemented by governments to limit the spread of the COVID-19 pandemic will produce significant economic consequences that are likely to exacerbate social and economic inequalities. In this paper we provide a framework to analyse how income inequality, besides other structural and policy-related features, shapes the trade-off between economic lockdown and contagion. We then supply empirical evidence, by means of simulation analysis, on the distributive effects of the lockdown for 31 European countries. Our results confirm that the lockdown is likely to significantly increase inequality and poverty and that the magnitude of the change is larger in more unequal countries. Such a cumulative process shapes a serious challenge for social and economic stability in the most vulnerable countries, which needs adequate policy response. However, the magnitude of the compensating measures is likely to be financially unsustainable, forcing them to lift necessary public health measures prematurely in order to avoid social collapse. This is likely to increase the risk of a new spread of the pandemic that might easily spill over to other countries. A supranational, coordinated health and fiscal policy effort is therefore in the interest of all economies willing to be part of a globalised economy.