We provide real-time evidence on the impact of Covid-19 restrictions policies on conflicts globally. We combine daily information on conflict events and government policy responses to limit the spread of coronavirus to study how conflict levels vary following shutdown and lockdown policies. We use the staggered implementation of restriction policies across countries to identify their effect on conflict incidence and intensity. Our results show that imposing a nationwide shutdown reduces the likelihood of daily conflict by around 9 percentage points. The reduction is driven by a drop in the incidence of battles, protests and violence against civilians. Across actors the decline is significant for conflicts involving political militias, protesters and civilians. We also observe a significant cross-country heterogeneity in the effect of restriction policies on conflict: no conflict reduction is observed in low income countries and in societies more fractionalized along ethnic or religious lines. We discuss the potential channels that can explain this heterogeneity.