In Germany, there is a vivid political debate on introducing a general statutory minimum wage. In this paper, we study the effects of minimum wages on labor supply using a structural household model where we distinguish between married and single households. In the model, labor supply of married women reacts positively and relatively strongly to minimum wages which we model as a wage subsidy as proposed in the German political debate. By contrast, other population subgroups show ambiguous reactions. An empirical analysis for Germany shows that minimum wages would affect total labor supply only weakly. Yet, in our baseline experiments, average labor supply of married women increases by 3-5%, whereas hours supplied by married female recipients of the minimum wage may increase by up to 28%. Further, we find that costs of a subsidized minimum wage increase sharply in its level while its effects on labor supply level out.