This paper presents a consensus-based distributed synchronization control method for microgrids with multiple points of interconnection. The proposed method can synchronize a microgrid at different points of interconnection using a common sparse communication network among its distributed generators. This functionality is critical for the networked operation of multiple microgrids in the future power systems. The proposed approach uses averaging and leader-follower modes of a commonly used consensus algorithm for multi-agent systems to achieve microgrid synchronization and smooth transition between the islanded and grid-connected modes at different interconnection points. The operation of the proposed distributed synchronization method is demonstrated on a microgrid with four inverters, each with an independent interconnection point to another microgrid or a bulk power system.