Background: The main purpose of this study was to evaluate the health services’ internal quality level in Greek public hospitals and to investigate whether there is a relation between internal quality and health care professionals’ job satisfaction. Material and Methods: A cross-sectional study was conducted in six public hospitals (four general and two specialized hospitals). The following tools were used to collect data: (a) the SERVQUAL questionnaire, which is designed to measure service quality through five dimensions, and (b) the Job Satisfaction Survey (JSS) questionnaire, which is designed to measure employees’ job satisfaction. Convenience sampling was used as a sampling technique. Results: The level of internal quality service was found to be low as regards the dimensions of: reliability, assurance, responsiveness, and empathy, while the “tangibles” dimension was the only one which was assessed as having a satisfactory internal quality level. Τhe results also revealed a positive correlation between the job satisfaction subscales and the quality dimensions. Regarding demographic characteristics and their effect on employees’ perceptions of internal quality dimensions, the study found that the gender and the educational factor had no effect while younger employees have a more positive perception of the quality of responsiveness dimension in the health organizations where they work. In terms of profession, administrative staff had a lower perception of the quality of tangibles dimension than doctors and nurses. Concerning years of experience, the results indicated that employees with more previous working experience had a worse perception of the quality of reliability, responsiveness, and assurance dimensions. Conclusions: According to the results, establishing a sense of trust and understanding between management and health professionals through effective communication, transparent evaluation, and reward is critical to developing, enhancing, and promoting an internal quality culture in a hospital setting.