Natural disasters such as hurricanes can cause substantial population out-migration. However, the magnitude of population movements is difficult to estimate using only traditional sources of migration data. We utilize data obtained from Facebook's advertising platform to estimate out-migration from Puerto Rico in the months after Hurricane Maria. We find evidence to indicate a 17.0% increase in the number of Puerto Rican migrants present in the US over the period October 2017 to January 2018. States with the biggest increases were Florida, New York and Pennsylvania, and there were disproportionately larger increases in the 15-30 age groups and for men compared to women. Additionally, we find evidence of subsequent return migration to Puerto Rico over the period January 2018 to March 2018. These results illustrate the power of complementing social media and traditional data to monitor demographic indicators over time, particularly after a shock, such as a natural disaster, to understand large changes in population characteristics.