In response to the SARS-CoV-2 pandemic, unprecedented travel restrictions and stay-at-home orders were enacted around the world. Ultimately, the public's response to announcements of lockdowns-defined as restrictions on both local movement or long distance travel-will determine how effective these kinds of interventions are. Here, we evaluate the effects of lockdowns on human mobility and simulate how these changes may affect epidemic spread by analyzing aggregated mobility data from mobile phones. We show that in 2020 following lockdown announcements but prior to their implementation, both local and long distance movement increased in multiple locations, and urban-to-rural migration was observed around the world. To examine how these behavioral responses to lockdown policies may contribute to epidemic spread, we developed a simple agent-based spatial model. Our model shows that this increased movement has the potential to increase seeding of the epidemic in less urban areas, which could undermine the goal of the lockdown in preventing disease spread. Lockdowns play a key role in reducing contacts and controlling outbreaks, but appropriate messaging surrounding their announcement and careful evaluation of changes in mobility are needed to mitigate the possible unintended consequences.