We provide the first causal analysis of how minimum wages affects enrollments and expenditures in the Supplemental Nutrition Assistance Program (SNAP). Exploiting state‐ and federal‐level variation in minimum‐wage policy between 1990 and 2012, and incorporating local controls in our specifications, we find that a 10 percent minimum wage increase reduces SNAP enrollment between 2.4 and 3.2 percent, and reduces program expenditures an estimated 1.9 percent. If the federal minimum wage were increased from $7.25 to $10.10, enrollment would fall between 7.5 and 8.7 percent (3.1 to 3.6 million persons) relative to 2012 levels, and annual expenditures would decrease 6 percent ($4.6 billion).