As the coronavirus pandemic spread across the globe in early 2020, the European Central Bank as well as national governments in the euro area enacted or announced numerous economic policy measures to counteract the severe economic consequences of the resulting lockdowns. In this paper, the immediate effect of the announcements on government bond and stock markets are estimated in a panel study. The results show that the ECB’s monetary policy measures barely had a stabilizing effect on the financial markets in the short term. With the exception of the announcement of Germany’s Economic Stabilization Fund, the fiscal rescue packages of other national governments and the EU did not lower government bond yields. In contrast, suspending fiscal rules and relaxing banking regulations had a calming effect on the markets, especially the government bond markets. In conjunction with fiscal policy measures, EU-wide measures in particular, they were able to stabilize the stock markets. Overall, the results show that policy action on the part of individual governments is not sufficiently effective on its own. To be effective, measures must be taken by Member States together. A joint crisis mechanism, such as the European Recovery Plan announced by the EU, could be quite efficient.