Social distancing can slow the spread of COVID-19 if citizens comply with it and internalize the cost of their mobility on others. We study how civic values mediate this process using data on mobility across Italian provinces between January and May 2020. We find that after the virus outbreak mobility declined, but significantly more in areas with higher civic capital, both before and after a mandatory national lockdown. The effect is not driven by differences in the risk of contagion, health-care capacity, geographic socioeconomic and demographic factors, or by a general North-South divide. Simulating a SIR model calibrated on Italy, we estimate that if all provinces had the same civic capital as those in top-quartile, COVID-related deaths would have been about 60% lower. We find consistent results for Germany where the incidence of the pandemic and restrictions to mobility were milder.