In Romania, influenza vaccination of healthcare professionals is recommended, but not mandatory. This study aims to investigate the attitudes and behaviors of medical students and resident physicians—the youngest healthcare professionals—towards influenza immunization, focusing on the barriers and facilitators, as well as on the impact of the COVID-19 pandemic. An anonymous online survey was conducted during the 2021/2022 influenza season, with responses from332 medical students and resident physicians. The majority (73.5%) were not vaccinated against influenza (68% of the students, 52.3% of the residents), although they were vaccinated against COVID-19 (94% students, 94.8% resident physicians) and believed that the pandemic positively influenced their attitude towards influenza vaccination. Vaccine accessibility (p < 0.001) and the necessity to pay for vaccination (p < 0.001) were identified as barriers in both groups, while lack of recommendation from a medical professional/teacher was significant only for students (p < 0.001). Forgetfulness and lack of prioritizations were the most cited reasons for not being vaccinated. These barriers could be diminished through proactive recommendation and simplification of the vaccination process, with accessible vaccination centers and implementation of vaccine reimbursement policies. Improved vaccination rates in young medical professionals are of the utmost importance both in their professional settings and as a model for the general population.