We examine the differential effects of minimum wages on immigrant and native workers in the United States. We find that minimum wage increases lead to reduced hours of work among immigrants with no effect on their employment. The effects are concentrated among recently-arrived, likely-undocumented workers in high turnover industries. Native workers show no such response, even when examining native subgroups with similar characteristics to the most affected immigrants. We conclude that affected immigrant labor markets feature low-surplus, low-investment employment relationships with flexible hours, but they are embedded in labor markets where replacement is unusually costly.