Medical students are in close contact with patients and should adhere to the same recommendations as healthcare workers. The study aimed to explore medical students' hesitancy towards COVID-19 vaccine and evaluate fear of COVID-19 and its relationship with hesitancy. A cross-sectional survey was conducted amongst a sample of medical students attending clinical years (November 2020–February 2021, Italy). Multivariable regressions were performed (p < 0.05 as significant). A total of 929 students participated (58.6% of eligible students). Hesitancy was reported by 6.7%; extreme fear of COVID-19 by 42.0%. Among hesitancy predictors, there were the survey completion before COVID-19 vaccine authorisation (adjOR = 6.43), adverse reactions after a vaccination (adjOR = 3.30), and receiving advice against COVID-19 vaccination from a relative (adjOR = 2.40). Students who received the recommended paediatric vaccinations (adjOR = 0.10), students with higher adherence to preventive measures (adjOR = 0.98), and students with fear of contracting COVID-19 with regard to the health of loved ones (adjOR = 0.17) were less likely to be hesitant. Females (adjOR = 1.85), students with poor health (adjOR = 1.64), students who had a loved one severely affected by COVID-19 (adjOR = 1.68), and students with fear of contracting flu (adjOR = 3.06) had a higher likelihood of reporting extreme fear. Hesitancy was remarkably lower than in similar studies. However, there is room for improvement in university activities that could deepen the competence in vaccines. Our focus on fear should not be overlooked, since the extent of extreme fear that we found might represent a substantial burden, considering the associations between fear and other health outcomes.