Healthcare facilities generate waste of various types and compositions, the majority of which is non-hazardous. Healthcare waste (HCW) quantity and composition by material-type are highly heterogeneous depending on such factors as types of healthcare facilities, seasonality and public health events (like epidemics), national HCW classification requirements, and integrated waste management practices (for example, reuse practices). Unfortunately, worldwide landfilling remains the predominant method for managing HCW, with infectious materials typically treated to eliminate infectivity prior to disposal. However, similar to waste generated in other sectors, HCW holds significant potential for successful valorization into new products, thereby reducing environmental impact, generating economic benefits, and aligning fully with the principles of the circular economy policy framework. Effective integration of healthcare waste into the circular economy requires a thorough analysis of its composition and material properties. In this study, infectious healthcare waste (iHCW) samples were collected from eight different healthcare facilities across Latvia, each utilizing either thermal or chemical inactivation methods for waste treatment. The composition of the waste, categorized by material type, was analyzed using instrumental testing methods. The compositional analysis from eight samples revealed that textiles (27–51%), primarily cellulose (25%), and plastics (16–54%), mainly polyester (17%) and polypropylene (15%), were the predominant components of iHCW across all types of healthcare facilities. Given the increasing importance of waste recovery technologies (for example, chemical recycling via pyrolysis or depolymerization), a thermochemical analysis was also conducted to determine the moisture, ash, and heating values of the two iHCW samples, respectively, one treated chemically and the second thermally. The thermochemical analysis results revealed a range of calorific values, encompassing both lower (13–23 MJ/kg) and higher (28–34 MJ/kg) values, due to the significant variability present in the composition of iHCW, along with variations in the moisture content (1–16 Maa; wt%) of the iHCW acquired after the disinfection process—thereby demonstrating the differences between iHCW that has been chemically disinfected and that which has been processed through rotoclaving. The results of this study provide valuable insights for circular economy practitioners regarding the potential of iHCW as a resource and for medical institution representatives in understanding how different waste types impact the environmental footprint of a healthcare facility.