Governments have developed and implemented various policies and interventions to fight the COVID-19 pandemic. COVID-19 vaccines are now being produced and distributed globally. This study investigated the role of good governance and government effectiveness indicators in the acquisition and administration of COVID-19 vaccines at the population level. Data on six World Bank good governance indicators for 172 countries for 2019 and machine-learning methods (K-Means Method and Principal Component Analysis) were used to cluster countries based on these indicators and COVID-19 vaccination rates. XGBoost was used to classify countries based on their vaccination status and identify the relative contribution of each governance indicator to the vaccination rollout in each country. Countries with the highest COVID-19 vaccination rates (e.g., Israel, United Arab Emirates, United States) also have higher effective governance indicators. Regulatory Quality is the most important indicator in predicting COVID-19 vaccination status in a country, followed by Voice and Accountability, and Government Effectiveness. Our findings suggest that coordinated global efforts led by the World Health Organization and wealthier nations may be necessary to assist in the supply and distribution of vaccines to those countries that have less effective governance.