This study develops a fractal-fractional epidemiological model to investigate the transmission dynamics of monkeypox. The existence, uniqueness, and stability of the model are established using fixed-point and Ulam-Hyers frameworks. A fractional Adams-Bashforth scheme is implemented for a numerical approximation, and simulations illustrate the role of memory and fractal effects in the disease spread. To enhance the predictive capability, the model is integrated with an Artificial Neural Network (ANN) and evaluated using publicly available datasets of outbreaks. Benchmarking against Caputo-derivative-based models demonstrates that the proposed approach achieves a superior goodness-of-fit, parameter identifiability, and short-term forecasting accuracy. These results highlight the potential of fractal-fractional modeling combined with machine learning to improve forecasting and inform control strategies for emerging epidemics.