Background: During the COVID-19 pandemic, the likelihood that hospital staff will report symptoms of depression, anxiety, and stress has increased. The aim of this study was to evaluate the relative influences of circumstantial, demographic, and trait–state anxiety variables on health anxiety in this group. Methods: A total of 168 hospital staff members (mean age: 28.91 years; 56.5% females) participated in the study. They completed a series of questionnaires covering sociodemographic characteristics, health anxiety, state–trait anxiety, and job-related information. Participants also reported whether they had close acquaintances (friends, family members) infected with COVID-19. Results: Higher health anxiety was related to both trait and state anxiety. Working on the frontline, being in contact with close acquaintances infected with COVID-19, and higher state and trait anxiety predicted higher health anxiety. Gender, age, and educational background were not predictors. Conclusions: In a sample of hospital staff, subjective feelings of anxiety about one own’s health were related to personality traits, individual experiences of having close acquaintances infected with COVID-19, and working on the frontline.