Medical and pharmaceutical products (MPP) are critical elements in humanitarian relief efforts. Relief operations are often burdened with inappropriate and unusable MPP, which leads to the wastage of resources and causes harm to the environment. This study investigates MPP management and facilitates the adoption of sustainability practices in the humanitarian medical supply chain. The study identifies 20 potential barriers for sustainability and categorises them into six different issues (material, operational, logistics, human, funding, and exogenous). Fuzzy best-worst method and analytic network process methodologies were adopted to prioritise barriers according to their degree of influence. Findings from the study suggest that stakeholders should focus attention on the material, operations, and logistical issues. Poor compliance with the World Health Organisation guidelines is reported as the most significant barrier to sustainability. Long-term collaboration and promotion of cash-based donation are suggested as suitable alternatives to product donation. The key recommendations of the study are to sensitise donors and media regarding donation practices and disaster relief victim requirements, build local capacity, design coordination mechanisms, and develop a performance measurement system incorporating the triple bottom line of sustainability. The study outcome reveals connections between barriers to sustainability and sheds light on the socioenvironmental aspect of donations. The study lays a foundation for future research, exploring how to better enable sustainability in the relief supply chain.