We report the characterization of microgap breakdown with perturbations from a metal rod floating between anode and cathode electrodes. The effects of the metal rod on the electric field distribution and the field enhancement factor are evaluated by numerical simulation and the conformal mapping method, and they indicate that the field emission regime is not reached. The breakdown voltages in the Townsend discharge regime are determined based on the voltage–current characteristics, which are obtained from two-dimensional fluid simulations. It is found that the breakdown characteristics can be significantly modulated by the floating metal rod, and the breakdown curve (breakdown voltage vs the net gap distance) is no longer U-shaped, which deviates from the conventional Paschen's law. The underlying physical mechanisms are related to the electric field enhancement, curved breakdown path, and nonuniform ion flux caused by the electric shielding effect. The results provide insights into breakdown characteristics in microscale discharges, which may promote conventional investigation of simplified clean gaps toward more complex conditions (e.g., with floating microparticles) in miniaturized plasma devices.