This paper highlights the role of supply chain linkages for the transmission of COVID-19 induced shocks based on the monthly trade of the European Union Member States during the first wave of the COVID-19 pandemic. Using the framework of the gravity model, we find an overall decline of over 20% in trade among EU countries following the COVID-19 outbreak. Both supply and demand shocks are shown to contribute to this trade decline associated with COVID-19 in the origin and destination country proxied by either infection rate or policy stringency index. While import demand shocks have an immediate effect on trade decline, the trade becomes increasingly sensitive to the COVID-19 situation in the origin country over time. Moreover, the results confirm that forward global value chain (GVC) linkages act as a channel for the transmission of (demand) shocks in supply chain trade. Indeed, an increase in the incidence of COVID-19 cases in the destination country leads to a larger decrease in domestic exports of intermediate goods in those destination countries with which a country has stronger forward linkages, i.e. in partners positioned further downstream. We also find the "China effect", with the transmission of the COVID-19 shock from the partner country amplified when the share of supply chain trade with China is higher. On the other hand, we fail to find robust evidence for the transmission of COVID-19-induced shocks via backward linkages.