Fear of becoming infected is an important factor of the complex suite of emotional reactions triggered by the COVID-19 pandemic. Among healthcare workers (HWs), fear of infection can put at risk their psychological well-being and occupational efficiency. The aim of this study was to analyze the role of personality (i.e., the big five traits) and adult attachment in predicting levels of fear (as measured by the FCV-19S) in 101 HWs employed in a COVID-19 university hospital. The three significant predictors retained by the stepwise regression model were age (beta = 0.26, t = 2.89, p < 0.01), emotional stability (i.e., the inverse of neuroticism) (beta = −0.26, t = −2.89, p < 0.01), and fearful attachment (beta = 0.25, t = 2.75, p < 0.01). Older HWs with higher levels of neuroticism and fearful attachment reported more intense fear of COVID-19. Our results can be useful to identify vulnerable subgroups of HWs and to implement selective programs of prevention based on counseling and psychological support.