The COVID-19 outbreak has demonstrated the diverse challenges that supply chains face to significant disruptions. Vaccine supply chains are no exception. Therefore, it is elemental that challenges to the COVID-19 vaccine supply chain (VSC) are identified and prioritized to pave the way out of this pandemic. This study combines the decision-making trial and evaluation laboratory (DEMATEL) method with intuitionistic fuzzy sets (IFS) to explore the key challenges of the COVID-19 VSC. The IFS theory tackles the uncertainty of key challenges while DEMATEL addresses the interlaced causal relationships among crucial challenges to the COVID-19 VSC. This work identifies 15 challenges and reveals that ‘Limited number of vaccine manufacturing companies’, ‘Inappropriate coordination with local organizations’, ‘Lack of vaccine monitoring bodies’, ‘Difficulties in monitoring and controlling vaccine temperature’, and ‘Vaccination cost and lack of financial support for vaccine purchase’ are the most critical challenges. The causal interactions along with mutual relationships among these challenges are also scrutinized, and implications for sustainable development goals (SDGs) are drawn. The results offer practical guidelines for stakeholders and government policy makers around the world to develop an improved VSC for the COVID-19 virus.