In this study, the spread of the monkeypox virus is investigated through the dynamical study of a novel Caputo fractional order monkeypox epidemic model. The interaction between human and rodent populations along with the effects of control signals are considered in the model. These control signals are established through the optimal control strategy. Furthermore, the effect of memory is examined via varying fractional order parameters in the model. The influences of other parameters are also examined. The positivity and boundness of the solution are verified through theoretical analysis. In addition, the equilibrium points for the system are obtained for both the free and endemic cases, and the local stability has been studied. To verify the theoretical findings, numerical experiments are conducted. The optimal control signals are obtained and verified through numerical simulations of different configurations of control parameters. From these simulations, it is found that the optimal control scheme can help in reducing the size of the infected, quarantined, and exposed categories while increasing the susceptible and recovered categories. These acquired results can provide some assistance to governments in providing some preventive control to suppress the spread of the virus.