Stress detection using physiological signals has emerged as a promising approach for monitoring mental health, yet current methods face significant challenges in preserving privacy while maintaining high accuracy. This paper introduces StressSentry-FHE, a novel privacy-preserving framework that leverages Fully Homomorphic Encryption (FHE) and Transformer-based architecture to analyze encrypted physiological data without compromising sensitive personal information. Our approach addresses critical limitations of existing models by: (1) implementing a specialized Transformer architecture that effectively captures complex inter-signal relationships and temporal dynamics across multiple physiological modalities including accelerometer, electrodermal activity, blood volume pulse, and temperature data; (2) developing FHE-compatible components through precision-preserving quantization strategies, numerically stable attention mechanisms, and efficient approximations for non-linear functions; and (3) delivering exceptional cross-subject generalization with 98.33% accuracy under General Partitioning and 96.06% accuracy with Leave-One-Subject-Out (LOSO) cross-validation on the WESAD 3-class dataset. Comparative analysis reveals that StressSentry-FHE significantly outperforms state-of-the-art approaches in both accuracy and privacy preservation, with only a modest 3.27% accuracy reduction when operating on fully encrypted data compared to plaintext inference. Our framework demonstrates that advanced deep learning architectures and robust privacy protection can be effectively combined for physiological signal analysis, establishing a new benchmark for secure affective computing in healthcare applications.