We investigate the distributed online economic dispatch (DOED) for microgrids, which typically consist of multiple bus nodes equipped with distributed generators and intelligent control units (ICUs), under time-varying supply–demand constraints. We formulate the DOED problem as a distributed online optimization problem with coupled inequality constraints. At each time step, each ICU has access only to its local cost function and local supply-demand constraints; ICUs make decisions online and cooperate to minimize the sum of the time-varying cost functions while satisfying global time-varying supply-demand constraints. We propose a distributed algorithm based on a primal-dual framework enhanced with the constraint-tracking technique. Under the assumption that the path length of the optimal generation output sequence grows sublinearly, we prove that both dynamic regret and constraint violation are sublinear with the time horizon T. Finally, we evaluate the proposed algorithm using both synthetic data and real-world data from the Australian Energy Market Operator. The results demonstrate that the proposed algorithm performs effectively in terms of tracking performance, constraint satisfaction, and adaptation to time-varying disturbances, thereby providing a practical and theoretically well-supported solution for DOED.