This paper analyzes whether a minimum wage should be used for redistribution on top of taxes and transfers. I characterize optimal redistribution for a government with three policy instruments -- labor income taxes and transfers, corporate income taxes, and a minimum wage -- using an empirically grounded model of the labor market with positive firm profits. A minimum wage can increase social welfare when it increases the average post-tax wages of low-skill labor market participants and when corporate profit incidence is large. When chosen together with taxes, the minimum wage can help the government redistribute efficiently to low-skill workers by preventing firms from capturing low-wage income subsidies such as the EITC and from enjoying high profits that cannot be redistributed via corporate taxes due to capital mobility in unaffected industries. Event studies show that the average US state-level minimum wage reform over the last two decades increased average post-tax wages of low-skilled labor market participants and reduced corporate profits in affected industries, namely low-skill labor-intensive services. A sufficient statistics analysis implies that US minimum wages typically remain below their optimum under the current tax and transfer system.