To contain the COVID-19 pandemic, governments introduced strict Non-Pharmaceutical Interventions (NPI) that restricted movement, public gatherings, national and international travel, and shut down large parts of the economy. Yet, the impact of the enforcement and subsequent loosening of these policies on the spread of COVID-19 is not well understood. Accordingly, we measure the impact of NPIs on mitigating disease spread by exploiting the spatio-temporal variations in policy measures across the 16 states of Germany. While this quasi-experiment does not allow for causal identification, each policy's effect on reducing disease spread provides meaningful insights. We adapt the Susceptible-Exposed-Infected-Recovered model for disease propagation to include data on daily confirmed cases, interstate movement, and social distancing. By combining the model with measures of policy contributions on mobility reduction, we forecast scenarios for relaxing various types of NPIs. Our model finds that in Germany policies that mandated contact restrictions (e.g., movement in public space limited to two persons or people co-living), closure of educational institutions (e.g., schools), and retail outlet closures are associated with the sharpest drops in movement within and across states. Contact restrictions appear to be most effective at lowering COVID-19 cases, while border closures appear to have only minimal effects at mitigating the spread of the disease, even though cross-border travel might have played a role in seeding the disease in the population. We believe that a deeper understanding of the policy effects on mitigating the spread of COVID-19 allows a more accurate forecast of disease spread when NPIs are partially loosened and gives policymakers better data for making informed decisions.