In this study, a fractional-order mathematical model is proposed to describe the transmission dynamics of Monkeypox using the Caputo fractional derivative, which effectively captures memory effects and long-range temporal dependencies inherent in disease spread processes. The population is divided into epidemiologically relevant compartments, and the qualitative behaviour of the resulting fractional system is rigorously investigated. Fundamental properties such as positivity and boundedness of solutions are established, ensuring the biological feasibility and well-posedness of the model. The basic reproduction number, R₀​, is derived using the next-generation matrix approach and is identified as a key threshold parameter that governs the persistence or extinction of the disease within the population. Local stability analysis reveals that the disease-free equilibrium is locally asymptotically stable when R₀<1, whereas for R₀>1, the system admits a unique endemic equilibrium that is also locally asymptotically stable. To reduce the disease burden while balancing the costs associated with intervention strategies, an optimal control problem is formulated by incorporating time-dependent controls representing vaccination of susceptible individuals, isolation of infectious cases, and treatment of infected individuals. The necessary conditions for optimality are derived using Pontryagin’s maximum principle, leading to a coupled system of state and adjoint equations. Numerical simulations based on the Adams–Bashforth–Moulton predictor–corrector method are performed to validate the analytical findings and demonstrate the effectiveness of the proposed control strategies in significantly reducing Monkeypox transmission.