Background and Objectives: A sustainability-oriented hospital governance has the potential to increase the efficiency of healthcare services and reduce the volume of expenses. The objective of this research is to develop a new complex tool for evaluating healthcare facility governance as a component of social responsibility, integrated into sustainability. Materials and Methods: We designed the research to develop the domains of a new reference framework for evaluating healthcare facility governance. The methodology for designing the indicators that make up the new reference framework consists of collecting and processing the most recent and relevant practices regarding the governance of healthcare facilities that have been reported by representative hospitals around the world. Results: We designed eight indicators that are brought together in the healthcare facility governance indicators matrix. They have descriptions and qualitative and quantitative rating scales with values from 0 to 5 that allow the degree of fulfillment to be quantified. The importance of the indicators is evaluated on a specific scale described qualitatively and quantitatively by values from 0 to 5. The values of the degree of achievement–importance couples of the indicators allow the development of improvement measures with priority according to the results revealed by the Eisenhower-type assessment diagram. Conclusions: Validation in practice of the system of indicators at an emergency hospital in an orthopedic profile highlighted the fact that they can be integrated into other national and international reference frameworks implemented in the hospital. The added value of the implementation consists of the facilitation of sustainable development and the orientation of health personnel, patients, and interested parties toward sustainability.