Drone strikes are a fixture of U.S. counterterrorism policy, often advertised as a ‘surgical’ alternative to ground operations. The effects of drone strikes, however, are somewhat less precise than proponents suggest. Using a dataset of over 12 billion call detail records from Yemen between 2010 and 2012, we show that the U.S. drone campaign significantly disrupted civilian lives in ways that previous studies do not capture. Strikes cause large increases in civilian mobility away from affected areas and create immediate and durable displacement: Mobility among nearby individuals increases 24% on strike days, and average distance from the strike region increases steadily for over a month afterward, signifying prolonged displacement for thousands of individuals. Strikes disrupt civilian life regardless of whether they kill civilians, though the effects are larger after civilian casualties. Our findings suggest that even carefully-targeted drone campaigns generate collateral disruption that has not been weighed in public debate or policy decisions about the costs and benefits of drone warfare.