We study the role of endogenous product market power in driving the equilibrium effects of the minimum wage. A higher minimum wage induces workers’ reallocation towards large firms, which increase their price markups as they gain market shares. We call this novel mechanism ``concentration channel" of the minimum wage. We build a novel structural model with frictional labor markets and oligopolistically-competitive product markets, which features endogenous markdowns and markups. We estimate the model on Italian social security data replicating the empirical wage distributions for each industry and worker skill type, as well as the concentration of detailed product markets. We find that both the aggregate labor share and value added are hump-shaped in the minimum wage size, owing to the countervailing response of markups and markdowns. We compute the optimal minimum wage, which trades off reallocation gains against employment losses from higher labor costs and markups. The optimal minimum wage in Italy equals 60% of the current median wage and induces welfare gains of 0.4% consumption equivalent units. Without endogenous product market power, the optimal wage would be higher and induce double welfare gains. Reduced-form evidence from Italian firms shows that the concentration channel matters for the firm-level adjustment to the minimum wage.