In view of rising wage and income inequality, the introduction of a legal minimum wage has recently become an important policy issue in Germany. We analyze the distributional effects of a nationwide legal minimum wage of 7.50 € 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, also taking into account potential employment effects as well as indirect effects on consumption. Simulation results show that the minimum wage would be rather ineffective in raising net household incomes and reducing income inequality, even if it led to a substantial increase in hourly wages at the bottom of the wage distribution. The ineffectiveness of a minimum wage in Germany is mainly due to the existing system of means-tested income support and the position of minimum wage earners in the income distribution.