Energy management in microgrids is typically formulated as a non-linear optimization problem. Solving it in a centralized manner not only requires high computational capabilities at the microgrid central controller (MGCC) but may also infringe customer privacy. Existing distributed approaches, on the other hand, assume that all the generations and loads are connected to one bus and ignore the underlying power distribution network and the associated power flows and system operational constraints. Consequently, the schedules produced by those algorithms may violate those constraints and thus are not feasible in practice. Therefore, the focus of this paper is on the design of a distributed energy management strategy (EMS) for the optimal operation of microgrids with consideration of the distribution network and the associated constraints. Specifically, we formulate microgrid energy management as an optimal power flow problem and propose a distributed EMS where the MGCC and the local controllers jointly compute an optimal schedule. As one demonstration, we apply the proposed distributed EMS to a real microgrid in Guangdong Province, China consisting of photovoltaics, wind turbines, diesel generators, and a battery energy storage system. The simulation results demonstrate that the proposed distributed EMS is effective in both islanded and grid-connected mode. It is also shown that the proposed algorithm converges fast.