The euro area, the countries that have adopted the euro, is converging some more towards a banking union. Starting from November 2014, the European Central Bank has become the single supervisor of euro zone banks calling for a more integrated supervision. Despite the on-going process, there are few studies that focus on the relationship between bank fragility and competition specifically for this economic block. Furthermore, it is not yet clear the extent of the relationship during a period of market turmoil and whether competition policies should account for the costs associated to systemic instability. We assess the relationship between market power and financial stability for the Eurozone banks over the period 2005-2012. We find that market power increases bank stability and it implies a net pecuniary cost after discounting for the cost of government intervention. We show that bank’s business model is significantly positively related to individual bank stability and that high market power is associated with lower stability during the recent market turmoil (2008-2012). Moreover, we advocate that capital injections and asset relief measures are effective and increase individual bank soundness.