We present a numerical study of a microelectromechanical-system-based design of a fiber cavity integrated with an ion-trap system. Each fiber mirror is supported by a microactuator that controls the mirror’s position in three dimensions. The mechanical stability is investigated by a feasibility analysis, which shows that the actuator offers stable support of the fiber. The actuators move the fibers’ positions continuously with a stroke of more than 10μ[my]m, with mechanical resonance frequencies on the order of kilohertz. A calculation of the trapping potential shows that a separation between the ion and the fiber consistent with strong ion-cavity coupling is feasible. Our miniaturized ion-photon interface constitutes a viable approach to integrated hardware for quantum information.