Graph-level anomaly detection (GLAD) aims to identify graphs that exhibit notable dissimilarity compared to the majority in a collection. However, current works primarily focus on evaluating graph-level abnormality while failing to provide meaningful explanations for the predictions, which largely limits their reliability and application scope. In this paper, we investigate a new challenging problem, explainable GLAD, where the learning objective is to predict the abnormality of each graph sample with corresponding explanations, i.e., the vital subgraph that leads to the predictions. To address this challenging problem, we propose a Self-Interpretable Graph aNomaly dETection model (SIGNET for short) that detects anomalous graphs as well as generates informative explanations simultaneously. Specifically, we first introduce the multi-view subgraph information bottleneck (MSIB) framework, serving as the design basis of our self-interpretable GLAD approach. This way SIGNET is able to not only measure the abnormality of each graph based on cross-view mutual information but also provide informative graph rationales by extracting bottleneck subgraphs from the input graph and its dual hypergraph in a self-supervised way. Extensive experiments on 16 datasets demonstrate the anomaly detection capability and self-interpretability of SIGNET.