Mental health AI systems typically require sensitive personal data to be transmitted to remote servers, creating significant privacy risks that deter user adoption. We propose a privacy-preserving framework that combines Federated Learning (FL) with Homomorphic Encryption (HE) to enable effective mental health prediction while keeping personal data on user devices. Our approach utilizes the CKKS encryption scheme within a federated architecture to train neural networks on distributed mental health datasets without compromising individual privacy. Experimental evaluation on a mental health dataset with 50 simulated clients demonstrates that our method achieves 66.2% accuracy for depression prediction while providing provable privacy guarantees. The system introduces only 2.3 s of encryption overhead per client update and successfully resists membership inference, property inference, and model inversion attacks. This work provides a practical solution for deploying AI-powered mental health applications that comply with healthcare privacy regulations while maintaining clinical effectiveness.