Interpretable brain network models for disease prediction are of great value for the advancement of neuroscience. GNNs are promising to model complicated network data, but they are prone to overfitting and suffer from poor interpretability, which prevents their usage in decision-critical scenarios like healthcare. To bridge this gap, we propose BrainNNExplainer, an interpretable GNN framework for brain network analysis. It is mainly composed of two jointly learned modules: a backbone prediction model that is specifically designed for brain networks and an explanation generator that highlights disease-specific prominent brain network connections. Extensive experimental results with visualizations on two challenging disease prediction datasets demonstrate the unique interpretability and outstanding performance of BrainNNExplainer.