The outbreak of the COVID-19 virus has led many states to take the drastic measures of social distancing. Using US executive order, occupation, and survey data, we measure the fall in labor supply due to these measures. Starting from a model of production networks, we analyze the sectoral effects of these labor shocks for the United States. We find that nonlinearities in the production network account for around half of the drop in GDP associated to the implementation of social distancing measures. The model also generates realistic dispersion in sectoral output change.