Voluntary physical distancing is essential for preventing the spread of COVID-19. We assessed the role of political partisanship in individuals' compliance with physical distancing recommendations of political leaders using data on mobility from a sample of mobile phones in 3,100 counties in the United States during March 2020, county-level partisan preferences, information about the political affiliation of state governors, and the timing of their communications about COVID-19 prevention. Regression analyses examined how political preferences influenced the association between governors' COVID-19 communications and residents' mobility patterns. Governors' recommendations for residents to stay at home preceded stay-at-home orders and led to a significant reduction in mobility that was comparable to the effect of the orders themselves. Effects were larger in Democratic- than in Republican-leaning counties, a pattern more pronounced under Republican governors. Democratic-leaning counties also responded more strongly to recommendations from Republican than from Democratic governors. Political partisanship influences citizens' decisions to voluntarily engage in physical distancing in response to communications by their governor.