We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.