The coordination of power distribution networks (PDNs) and microgrids (MGs) is challenging due to the abundant resources and their dispersed geographical distribution, making centralized computation inefficient. To address this issue, we propose a coordination framework with single leader and multiple followers that allows limited information exchange. In this framework, the PDN operators act as leaders, while the MG operators act as followers. However, variations in load and renewable energy during MG scheduling intervals can cause variability in power transactions between PDNs and MGs. This variability can reduce the net revenue of MGs and increase the operation costs of PDNs, which makes it essential to consider the worst-case fluctuations. We introduce a multi-agent robust deep reinforcement learning (MARDRL) approach for coordination of PDNs and MGs, accounting for the worst-case scenarios. The numerical results on the test systems verify the effectiveness of the proposed approach in enhancing the coordination of PDNs and MGs.