In recent years, the DC distribution network based on MMC is developing rapidly. However, DC side fault protection has become an urgent problem because of the sharply rising overcurrent generated by short circuit and the poor overcurrent capacity of power electronics. Considering the two different topologies of half-bridge and full-bridge MMC, the fault characteristics are analyzed and the analytical expressions of fault voltage and current are derived respectively when a bipolar short circuit occurs on medium voltage DC lines. For the half-bridge MMC, a protection strategy based on bridge arm current-limiting module and DC circuit breaker is proposed, which solves the problem of slow fault current attenuation and excessive steady current, and thus reduces the requirement for the breaking capacity of the DC circuit breaker. Based on the fault current self-clearing capability of the full-bridge MMC sub-module, an improved fast recovery protection strategy is proposed to reduce the system outage time by unlocking the MMC. Finally, the PSCAD/EMTDC simulation results prove the effectiveness and practicability of the protection strategy based on the actual engineering parameters.