German hospitals are now confronted with major challenges from both shortages and fluctuations in the numbers of physicians and nurses. This makes it even more important that physicians and nurses do not prematurely leave patient care. The objective of the present study was to improve our understanding of the factors that trigger intentions to leave the profession. For this purpose, data from 1060 young physicians and nurses in hospital care were analysed. Intentions to leave the profession was assessed with the Copenhagen Psychosocial Questionnaire (COPSOQ). In the first step, the association was determined between intention to leave the profession and the factors of perceived quality of care and job satisfaction. In a second step, a mediation analysis was performed to determine the effect of perceived quality of care after correction for the possible mediator of job satisfaction. There were statistically significant negative associations between perceived quality of care and intention to leave the profession (beta: −2.9, 95% CI: −4.48–−1.39) and job satisfaction and intention to leave the profession (beta: −0.5, 95% CI: −0.64–−0.44). The effect of perceived quality of care on intention to leave the profession was partially mediated by job satisfaction. Thus, high perceived quality of care and high job satisfaction are both important factors that tend to prevent young physicians and nurses from leaving their professions.