Healthcare services create medical waste that may be dangerous to healthcare personnel, patients, the general public, and the environment. Medical waste disposal method selection is among the most important decisions that must be made by healthcare organizations, and such a problem has a number of contradictory criteria and alternatives. On the other hand, decision experts may have considerable uncertainty while evaluating these alternatives. In this paper, new fuzzy multi-criteria decision-making (MCDM) methodologies are provided for assessing the medical waste disposal alternatives. The CRiteria Importance Through Intercriteria Correlation (CRITIC) is used for obtaining criterion weights in an objective manner, and the Weighted Aggregated Sum Product ASsessment (WASPAS) approach is utilized to rank the alternatives. For modeling the uncertainty in the nature of the problem, the proposed methodology is developed in single and interval-valued spherical fuzzy environments. Single-valued spherical fuzzy sets enable users to model the membership, non-membership, and hesitancy parameters independently. On the other hand, interval-valued spherical fuzzy sets provide increased fuzziness modeling capacity. The step-by-step solution of the proposed methodologies are followed by sensitivity and comparative analyses, and a discussion. This study contributes to the work of both academics and practitioners in the healthcare industry, as well as other sectors facing similar types of decision-making problems.