Many papers have focused on the effect of national policies on the fall of the rate of COVID-19 cases. However, the effect of national policies on COVID-19 shocks coming from abroad is still an open question. This paper uses daily new confirmed COVID-19 cases from May 2020 to March 2022 in 36 countries, including OECD countries and China, and a high-dimensional method to measure and study the international connectedness of COVID-19. Our main result shows that national policies such as international travel restrictions were effective in reducing the connectedness of COVID-19 from abroad before the wide availability of the vaccines, but not when the vaccine was first made available to the public. We also show that larger distances between two countries multiplied the effect of national policies on connectedness from another country, while common languages dampened it. The results of this paper could help policymakers in a trade-off analysis between containment policies and socioeconomic costs.