Vaccination against COVID-19 is a highly debated subject that brings confusion due to contradictory information coming from the scientific community and the media. Our aim was to focus on a homogeneous group of students in the healthcare field to assess their intention to vaccinate and the drivers behind this decision. A cross-sectional study was performed in the spring of 2021 in a Medical University in Romania. 725 of the undergraduates that completed an online questionnaire regarding their intention to vaccinate against COVID-19 were included in the study. Univariable analysis and logistic regression were performed on several variables to analyze factors affecting the willingness to vaccinate against COVID-19. In our study sample, 93.1% of students presented a strong intention to vaccinate, out of which the highest proportion belonged to subjects studying general medicine (96%). On logistic regression, we identified the following predictor factors: previous infection with coronavirus, prior vaccination refusal, VAX score, scientifically oriented sources of information and preference for RNA-based technology. Medical students have an increased willingness towards vaccination. Even for them, a highly educated and informed group of subjects, the general attitude towards vaccinations has a strong impact on the choice of COVID-19 vaccination.