What is the impact of the minimum wage on the college wage premium? I show that job-ladder models imply that the effect should be small on impact--raising only the wages of workers bound by the minimum wage--and grow over time as workers slowly move up the job ladder. Guided by my theory, I present evidence that these dynamic effects are present and powerful. Estimated at the national level, I show that minimum wages--together with supply and demand--play a central role in shaping the evolution of the U.S. college premium. Estimated at the state level, I show that the elasticity of the college premium to the minimum wage is small on impact and grows dramatically over time. To verify my theory's mechanisms, I additionally document the dynamic impact of the minimum wage over the full wage distribution: on impact, wages rise only for the lowest percentiles (consistent with the literature) but over time this effect spills over up the wage distribution (consistent with my theory and my empirical results on the skill premium). On the basis of these theoretical and empirical results, I conclude that the minimum wage plays a central role in shaping the U.S. college premium and its variation across states.