Background: Spirituality has emerged as a potential protective factor that may promote mental well-being and resilience among healthcare workers. Aim: This study aims to examine the relationship between spirituality, stress, and depression among healthcare professionals in Greece. Methods: This cross-sectional study surveyed 412 employees at the Corinth General Hospital in Greece, including medical, nursing, and administrative personnel. The data were collected using the Functional Assessment of Chronic Illness Therapy—Spiritual Well-Being 12 (FACIT-SP12), the Perceived Stress Questionnaire (PSQ), and the Center for Epidemiologic Studies Depression Scale (CES-D). The statistical analyses included non-parametric tests, correlation coefficients, and multiple regression. Results: The mean spirituality score was 34.6 (±6.83), while the stress and depression scores were 74.6 (±14.87) and 14.7 (±10.20), respectively. Spirituality was significantly and negatively correlated with both stress (r = −0.479, p < 0.001) and depression (r = −0.452, p < 0.001). Gender, years of service, educational level, and marital status were also associated with variations in stress, depression, and spirituality levels. Women and those with lower education reported significantly higher levels of stress and depression. Additionally, some demographic variables such as age and sector of employment did not show significant associations with spirituality or depression. The regression analysis confirmed spirituality as an independent predictor of lower stress levels (B = −1.158, p < 0.001). Conclusions: Spirituality is a significant predictor in mitigating stress and depression among healthcare workers. Promoting a supportive spiritual climate and incorporating elements of spiritual leadership in healthcare settings may enhance employee well-being and resilience. Future research should expand on these findings across diverse institutional and cultural contexts.