This paper shows that more highly concentrated labor markets experience more positive employment effects of the minimum wage. In the most concentrated labor markets, employment rises following a minimum wage increase. The paper establishes its main findings studying the effects of local minimum wage increases on a key low-wage retail sector, and using data on labor market concentration that covers the entirety of the United States with fine spatial variation at the occupation level. The results carry over to the fast-food sector and the entire low-wage labor market, and are robust to using proxies of labor market concentration available for a broader range of industries, such as the number of establishments and population density. A model of oligosponistic competition can explain these effects: there is more room to increase wages in high concentration areas where wages tend to be further below marginal productivity. These findings provide evidence supporting monopsonistic wage setting as an explanation for the near-zero minimum wage employment effect documented in prior work.