Countries have sought to stop the spread of coronavirus disease 2019 (COVID-19) by severely restricting travel and in-person commercial activities. Here, we analyse the supply-chain effects of a set of idealized lockdown scenarios, using the latest global trade modelling framework. We find that supply-chain losses that are related to initial COVID-19 lockdowns are largely dependent on the number of countries imposing restrictions and that losses are more sensitive to the duration of a lockdown than its strictness. However, a longer containment that can eradicate the disease imposes a smaller loss than shorter ones. Earlier, stricter and shorter lockdowns can minimize overall losses. A 'go-slow' approach to lifting restrictions may reduce overall damages if it avoids the need for further lockdowns. Regardless of the strategy, the complexity of global supply chains will magnify losses beyond the direct effects of COVID-19. Thus, pandemic control is a public good that requires collective efforts and support to lower-capacity countries.