The objectives of this study were to obtain information on medical students’ attitudes toward COVID-19 vaccination and to identify the main barriers to its acceptance. We conducted an anonymous online survey on a sample of undergraduate medical students from one main Italian University. The questions were aimed at exploring their attitudes toward vaccination to prevent COVID-19, their perceptions of the risk/threat of COVID-19 and the factors associated with their attitudes toward COVID-19 vaccination. A high percentage of students in our sample stated that they had been vaccinated or that they intended to be vaccinated against the COVID-19 coronavirus. A total of 239 questionnaires were analyzed. Age, social, geographic and demographic characteristics, health conditions and interest in vaccination were recorded; 93% of the students declared that they encouraged vaccination and 83% stated that the reason was “Moral responsibility towards the community”. Four students had not yet been vaccinated, mainly because of “Contradictory information on efficacy and safety”. The Likert-type questions revealed high agreement on the importance of vaccination and whether it should be made mandatory (“indispensable tool” and “ethical duty” were cited to explain this position). The results show a high level of acceptance of COVID-19 vaccination among these medical undergraduates who, being halfway through their training and involved in clinical practice, are already in possession of specific scientific knowledge and, to a small extent, come from different areas of Italy.