The global spread of the novel coronavirus (COVID-19) has accounted for many deaths. The effective containment of the current COVID-19 epidemic calls for a fast and sustainable delivery strategy to minimize the impact of this crisis. As such, this study aimed to conduct a comprehensive review of research on the vehicle routing problem (VRP) from a sustainable viewpoint during the pandemic and explore viable delivery solutions that may aid in the containment of the COVID-19 pandemic. Through a systematic review of the selected articles, four broad themes of pandemic containment measures from the delivery aspect were identified: efficient pharmaceutical delivery strategy, contactless distribution, sustainable waste transportation strategy, and isolated and quarantine vehicle scheduling. Following that, the methodology utilized to execute the containment measures were analyzed, research gaps were hightlighted, and possibilities for future studies were suggested. In summary, the goal of this research is to provide an overview of the literature on the application of VRPs in pandemic control and to assist academics and practitioners in learning more about the performance metrics, models, and solution techniques utilized in pandemic control delivery operations.