The mobility of damaged chromatin regions in the nucleus may affect the probability of mis-repair. In this work, live-cell observation and distance tracking of GFP-tagged DNA damage response protein MDC1 was used to study the random-walk behaviour of chromatin domains containing radiation-induced DNA double-strand breaks (DSB). Our measurements indicate a subdiffusion-type random walk process with similar time dependence for isolated and clustered DSBs that were induced by 20 MeV proton or 43 MeV carbon ion micro-irradiation. As compared to normal diffusion, subdiffusion enhances the probability that both ends of a DSB meet, thus promoting high efficiency DNA repair. It also limits their probability of long-range movements and thus lowers the probability of mis-rejoining and chromosome aberrations.