Our paper empirically investigates the role of economic cooperation involving trade in coronavirus disease (COVID-19)-related essential medical goods—vaccines and their value chains, personal protective equipment, and diagnostic test kits—across 29 Asia and the Pacific economies. The paper incorporates vaccines and their global value chain products trade for the first time in the empirical literature. We further investigate whether trade facilitation, proxied by membership in regional trade agreements (RTAs), can help mitigate any adverse impact on trade in essential medical goods, applying a structural gravity framework. The results confirm that while trade is critical for Asian economies, its nature differs. Low-income economies are largely dependent on imports, whereas selected middle- and high-income economies are part of two-way trade and engaged in the low end of the vaccine value chain. We find that the onset of the pandemic has hurt exports of these goods. This adverse effect is found to be lowered for economies engaged in RTAs. This emphasizes the role of governments in committing to RTAs and implementing trade facilitation measures.