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Economic dispatch in a multi-microgrid (MMG) system involves an increasing number of states from distributed energy resources (DERs) compared to a single microgrid. In these cases, traditional reinforcement learning (RL) approaches may become computationally expensive or less effective in finding the least-cost solution. This paper presents a novel RL approach that employs local learning agents to interact with individual microgrid environments in a distributed manner and a global agent to search for actions to minimize system cost at the MMG system level. The proposed distributed RL framework is more efficient in learning the dispatch policy compared to conventional approaches. Case studies are performed on a 3-microgrid system with different types of DERs. Results substantiate the effectiveness of the proposed approach in comparison with conventional methods in terms of operation costs, computation time, and peak-to-average ratio.