Early detection of mental health risks plays a critical role in preventing long-term psychological disorders and enabling timely interventions. However, existing predictive models often operate as black boxes, limiting transparency and trust in decision-making. In this study, we propose a Neuro-Symbolic AI-driven framework that integrates data-driven machine learning with symbolic reasoning to achieve rule-based interpretability in mental health risk prediction. The pipeline involves robust preprocessing, outlier removal, feature selection, and class balancing, followed by training multiple classifiers, including Random Forest, Logistic Regression, Decision Tree, MLP, and Extra Trees. To enhance transparency, we extract human-readable rules from the Decision Tree and incorporate them into an interactive Flask-based dashboard for real-time risk assessment and decision support. Experiments conducted on a dataset of 10,000 participants demonstrate strong predictive performance, with the Random Forest model achieving an accuracy of 99.26%. This work bridges predictive accuracy with transparent rule-based reasoning, providing a novel and practical tool for clinicians, researchers, and policymakers working in mental health analytics.