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We study the macroeconomic effects of the COVID-19 epidemic in a quantitative dynamic general equilibrium setup with nominal rigidities. First, we evaluate various containment policies and show that they allow to dramatically reduce the welfare cost of the disease. Then we investigate the role that monetary policy, in its capacity to manage aggregate demand, should play during the epidemic. According to our results, treating the observed output contraction as a standard recession leads to a bad policy, irrespective of the underlying containment measures. We evaluate how monetary policy should resolve the trade-off between stabilizing the economy and containing the epidemic. We find that containment policies and monetary policy are complementary. If no administrative restrictions are implemented, the second motive prevails, and, despite the deep recession, optimal monetary policy is contractionary. Conversely, if sufficient containment measures are introduced, central bank interventions should be expansionary and help stabilize economic activity.