The municipalities of Minas Gerais face significant challenges in managing public resources allocated to health, due to financial constraints and social disparities. These difficulties reinforce the need for an understanding of the effectiveness of resource allocation in the public health sector. By adopting Shannon Entropy for efficiency assessment, this methodology enhances the analysis to consider the variability and uncertainty inherent in the data, thus enabling an understanding of the nuances regarding the distribution of resources for health. This study conducts a comprehensive investigation into the efficiency of public health spending, employing Shannon Entropy as a weighting method in the calculation of Efficiency. The main objective is to provide an in-depth assessment of the effectiveness of resource allocation in the public health sector. The results obtained reveal a new perspective on the allocation of resources for health, highlighting specific areas for potential improvement and optimization, essential to increase the overall efficiency of public health spending. This robust framework serves as a valuable tool for public policymakers, facilitating decision-making processes and ensuring the effective use of public resources for health. The main contribution of this study focuses on the application of Shannon Entropy to efficiency analysis, which not only improves the understanding of public health spending but also provides a new perspective for optimizing resource allocation in the health sector.