Vaccinations for the prevention of coronavirus disease (COVID-19) are important to control the ongoing pandemic. A much-discussed strategy to increase vaccination coverage is mandatory vaccination; however, its legitimacy and effectiveness as a measure are doubtful. This study aims to investigate the attitudes of the general population of Cyprus towards COVID-19 mandatory vaccination and to identify the factors influencing individuals’ attitudes towards such policy. An online cross-sectional study was conducted, using a self-administered, anonymous questionnaire to collect information on sociodemographic and health-related characteristics, trust, and satisfaction about the healthcare system and utilization of preventive healthcare services, COVID-19 vaccination information, general vaccination knowledge, and attitudes towards mandatory vaccination. A total of 2140 participants completed the survey, with 27.8% being in favor of mandatory vaccination. We found that as the age increases by one year, the odds of supporting mandatory vaccination increase by 1.04 units (OR 1.04, 95% CI: 1.02–1.05). In addition, those who reported increased trust in national healthcare authorities’ guidelines and recommendations (OR 3.74, 95% CI: 3.11–4.49) and those satisfied with the healthcare system (OR 1.38, 95% CI: 1.16–1.65) and follow doctor’s instructions (OR 1.29, 95% CI: 1.03–1.61), were significantly more likely to support mandatory vaccination while those who had underage children living in the household were significantly less likely to support mandatory vaccination (OR 0.69, 95% CI: 0.50–0.94). Public health authorities need to develop well-organized vaccination campaigns in which accurate evidence-based information would be disseminated with respect to individuals’ autonomy.