Graph neural networks (GNNs) have achieved great success in many research areas ranging from traffic to computer vision. With increased interest in cloud-native applications, GNNs are increasingly being investigated to address various challenges in microservice architecture from prototype design to large-scale service deployment. To appreciate the big picture of this emerging trend, we provide a comprehensive review of recent studies leveraging GNNs for microservice-based applications. To begin, we identify the key areas in which GNNs are applied, and then we review in detail how GNNs can be designed to address the challenges in specific areas found in the literature. Finally, we outline potential research directions where GNN-based solutions can be further applied. Our research shows the popularity of leveraging convolutional graph neural networks (ConGNNs) for microservice-based applications in the current design of cloud systems and the emerging area of adopting spatio-temporal graph neural networks (STGNNs) and dynamic graph neural networks (DGNNs) for more advanced studies