We argue that the arrival of immigrants with low reservation wages can strengthen the monopsony power of firms. Firms can exploit "cheap" migrant labor by offering lower wages, though at the cost of forgoing potential native hires who demand higher wages. This monopsonistic trade-off can lead to large negative effects on native employment, which exceed those in competitive models, and which are concentrated among low-paying firms. To validate these predictions, we study changes in wage premia and employment across the firm pay distribution, during a large immigration wave in Germany. These adverse effects are not inevitable, and may be ameliorated through policies which constrain firms' monopsony power over migrants.