We present an efficient parallel algorithm for statistical Molecular Dynamics simulations of ion tracks in solids. The method is based on the Rare Event Enhanced Domain following Molecular Dynamics (REED-MD) algorithm, which has been successfully applied to studies of, e.g., ion implantation into crystalline semiconductor wafers. We discuss the strategies for parallelizing the method, and we settle on a host-client type polling scheme in which a multiple of asynchronous processors are continuously fed to the host, which, in turn, distributes the resulting feed-back information to the clients. This real-time feed-back consists of, e.g., cumulative damage information or statistics updates necessary for the cloning in the rare event algorithm. We finally demonstrate the algorithm for radiation effects in a nuclear oxide fuel, and we show the balanced parallel approach with high parallel efficiency in multiple processor configurations.