Medical students may come in contact with individuals infected with COVID-19 in their clinical rotations. A high level of acceptance of vaccination is needed for them to protect their health and the health of patients from this disease. The objectives of this study were to (1) obtain information on medical students’ attitudes toward COVID-19 vaccination, (2) assess factors associated with students’ attitudes, and (3) identify predictors of their willingness to receive a third dose of the COVID-19 vaccine. Using a cross-sectional design, we conducted a questionnaire survey of medical students in July 2021. For this survey, we employed a 15-item questionnaire specifically developed to assess the students’ attitudes toward COVID-19 vaccination. Of the 742 distributed questionnaires, 496 (294 males and 202 females) were completed. Among all the participants, 89.1% (442/496) received the second dose of the vaccine, and 90.7% (450/496) indicated that they would hypothetically receive the COVID-19 vaccine in the future. Furthermore, 84.5% (419/496) of all the participants were willing to receive a third dose of the vaccine. Regarding willingness to receive a third dose of the COVID-19 vaccine, multiple logistic regression models showed that students’ grade and their responses to Q1 (positive attitude toward vaccination), Q9 (belief in the protection offered by COVID-19 vaccination), Q10 (concern about the excessively rapid development of COVID-19 vaccines), Q12 (need for aspects of pre-pandemic life), and Q14 (concern about the sustainability of immunity) had significant associations with this outcome. Confidence in vaccines, relaxation of mobility restrictions, and concern about the sustainability of immunity motivate willingness to receive a third dose of the COVID-19 vaccine in medical students.