The coronavirus pandemic has been recognized as a major threat to public health. Widespread acceptance of COVID-19 vaccines is crucial for achieving adequate immunization coverage to end the global pandemic. However, to date, there are still hesitant people, especially among the younger population groups. For this reason, it is essential to identify the psychological variables that may affect vaccination intention among these “at risk groups” and to select possible successful communication frames in order to increase vaccination rates. An online cross-sectional survey was carried out on 208 Italian citizens younger than 50 years old, to explore message framing effects on their intention to receive the vaccination and to understand the psychological factors influencing it. Results showed that depending on the goal (stimulate vaccination intention, vaccination trust, or vaccine attitude), not all the communication stimuli are equally effective on this target population. Furthermore, the study showed that sociodemographic variables do not help to explain the vaccination intention of the younger population groups, while the psychological variables have been found to have a stronger impact on such attitude. Trust and attitudes towards vaccines, concern about the pandemic and concern about infecting others have been found to be the most effective predictive variables of people vaccination intention. The study results underline the importance of understanding the psychological roots behind vaccine hesitancy to shape sensitization actions and vaccination campaigns targeting this population group.