Introduction: As of March 2020, coronavirus disease 2019 (COVID-19) has been declared a “pandemic” by the WHO. This has led to the need for governments around the world to implement restrictive containment and isolation measures to stem the spread of the virus; these measures have included social distancing, isolation, and quarantine. The fear of contagion has been indicated as one of the causes of stress, anxiety, depression, and insomnia in the general population. With respect to the response of young people to the pandemic, the category of University students deserves further attention. The sudden change in “University” habits (i.e., poor interaction with teachers and colleagues, disturbing learning environment, and difficulty in adapting to online learning), the consequent loss of a social network, and the economic problems in their families have seriously affected the psychophysical well-being of University students. The aim of this study was to explore, in a sample of Italian University students, the relationships among anxiety, perceived vulnerability to disease, and smartphone use during the COVID-19 pandemic.Methods: A sample of 194 volunteer college students (i.e., 86 males and 108 females) aged between 18 and 30 years (M = 21.74; SD = 2.39) were recruited to participate in this study. Participants were recruited through an online questionnaire sent to students of the University of Catania, Italy, and distributed from September 2020 to January 2021. The volunteer participants were given an online protocol that included the Fear of COVID-19 Scale (FCV-19S) for the evaluation of fear, the Perceived Vulnerability to Disease (PVD) for the evaluation of perceived vulnerability to disease, the State-Trait Anxiety Inventory (STAI) for the evaluation of trait and state anxiety, and the Smartphone Addiction Scale Short Version for Adolescents and Young Adults (SAS-SV) for the evaluation of use, abuse, or addiction of smartphone use.Results: The fear of COVID-19 did not reach an intensity such as to be defined as serious (i.e., fear score: 15.53) in the whole sample. Both men and women showed a high risk of smartphone addiction (i.e., score of males: 28.33 and score of females: 26.88) in SAS-SV. University students showed moderate trait and state anxiety [i.e., a score of 51.60 in Trait Anxiety Inventory (TAI) and a score of 47.21 in State Anxiety Inventory (SAI)] in STAI. In addition, students showed moderate perceived vulnerability to disease (i.e., a score of 51.51) in PVD. The results showed that fear of COVID-19 and trait anxiety appear to be the predictors of SAI and PVD but not the predictors of risk of smartphone addiction (SAS-SV).Conclusions: The data highlighted the presence of a perception of vulnerability to infections in subjects in which there was also a moderate anxiety, both state and trait, associated with the fear of the COVID-19 pandemic. It is hoped that a large part of the population will soon be vaccinated, including University students, and therefore, it would be desirable to carry out further assessments in the post-vaccine phase to highlight any differences in the state of anxiety and the perception of vulnerability to infections. The possible positive role of the use of smartphones in maintaining social contacts should also be emphasized.