University students are a vulnerable population and faced a significant psychological impact from the COVID-19 pandemic. Therefore, this study aimed to determine the level of fear of COVID-19 among university students and to evaluate the possible relationship between fear of COVID-19 and socio-demographic, health-related determinants, variables related to the COVID-19 and variables related to the psychological impact of the COVID-19 pandemic. We conducted a cross-sectional study between December 2020 and December 2021 on a sample of 950 university students from two universities in southern Spain. Participants completed a form that collected socio-demographic, health-related and COVID-related variables, a validated questionnaire related to the psychological impact of the COVID-19 pandemic and the fear of COVID Scale (FCV-19S). Descriptive, inferential, and multivariable linear regression analyzes were conducted. The mean FCV-19S score was 14.86 ± 5.16 points. The factors identified as predictors of FCV-19S were being female (p < 0.001), holding religious beliefs (p = 0.04), living in towns with over 10,000 inhabitants (p < 0.01), living with someone vulnerable to COVID-19 (p = 0.02), watching TV to keep informed about COVID-19 (p < 0.01), believing in a low probability of surviving if infected with COVID-19 (p < 0.001), having a higher level of death anxiety (p < 0.001) and suffering from insomnia (p < 0.001). An average fear of COVID-19 score of 14.86 ± 5.16 points has been found among university students in Spain. These findings can aid in identifying specific factors contributing to fear of COVID-19 and in developing coping strategies to alleviate the stress of the pandemic.