In view of rising wage inequality and increasing poverty, the introduction of a legal minimum wage has recently become an important policy issue in Germany. We analyze the distributional effects of the introduction of a nationwide legal minimum wage of € 7.5 per hour on the basis of a microsimulation model which accounts for the complex interactions between individual wages, the tax-benefit system and net household incomes. Simulation results show that the minimum wage would be rather ineffective in reducing poverty, even if it led to a substantial increase in hourly wages at the bottom of the wage distribution and had no negative employment effects. The ineffectiveness of a minimum wage in Germany is mainly due to the existing system of means-tested income support.