Adverse Drug Reaction (ADR) is a significant public health concern world-wide. Numerous graph-based methods have been applied to biomedical graphs for predicting ADRs in pre-marketing phases. ADR detection in post-market surveillance is no less important than pre-marketing assessment, and ADR detection with large-scale clinical data have attracted much attention in recent years. However, there are not many studies considering graph structures from clinical data for detecting an ADR signal, which is a pair of a prescription and a diagnosis that might be a potential ADR. In this study, we develop a novel graph-based framework for ADR signal detection using healthcare claims data. We construct a Drug-disease graph with nodes representing the medical codes. The edges are given as the relationships between two codes, computed using the data. We apply Graph Neural Network to predict ADR signals, using labels from the Side Effect Resource database. The model shows improved AUROC and AUPRC performance of 0.795 and 0.775, compared to other algorithms, showing that it successfully learns node representations expressive of those relationships. Furthermore, our model predicts ADR pairs that do not exist in the established ADR database, showing its capability to supplement the ADR database.