The application of a quantum-inspired firefly algorithm was introduced to obtain optimal power quality monitor placement in a power system. The conventional binary firefly algorithm was modified by using quantum principles to attain a faster convergence rate that can improve system performance and to avoid premature convergence. In the optimization process, a multi-objective function was used with the system observability constraint, which is determined via the topological monitor reach area concept. The multi-objective function comprises three functions: number of required monitors, monitor overlapping index, and sag severity index. The effectiveness of the proposed method was verified by applying the algorithm to an IEEE 118-bus transmission system and by comparing the algorithm with others of its kind.