Background/Objectives: Hospitalization among older adults represents an increasingly significant challenge in Mexico due to the high prevalence of chronic diseases and the current strain on the country’s public healthcare services. This study aims to develop a predictive model for hospitalization using longitudinal data from the Mexican Health and Aging Study (MHAS) using the Random Forest (RF) algorithm. Methods: Three machine learning models based on RF were designed and evaluated under different data partition configurations, with and without interaction between inputs. The models were validated using nested cross-validation to ensure robustness and prevent overfitting. Evaluation metrics included sensitivity, specificity, and the kappa coefficient, along with their respective standard errors. Results: The M2 model, which included interaction and a 20% test proportion, achieved the best balance between sensitivity (0.7215, standard error ±0.0038) and specificity (0.4935, standard error ±0.0039), despite the imbalance in the dataset and the heterogeneity of the population. This ability of the model to balance performance allows it to handle the complexities of predicting hospitalizations well across different patient profiles. Conclusions: The M2 model shows great potential for clinical application by enabling the anticipation of hospital demand and enhancing resource planning. This suggests substantial benefits for healthcare systems, particularly in optimizing the care of older adults. Future research will focus on integrating subgroups based on comorbidities and applying advanced techniques for handling missing data to further optimize predictive capacity.