Roughly 789 million people have no access to energy, and around 2.8 billion people lack access to clean cooking solutions according to the World Bank, and so we also find many people that cannot afford energy (reliable and clean) at the current prices. In the literature, accessibility, availability, and affordability are underlined as the key drivers of energy poverty. In South America, these aspects have not been studied in depth. This research is relevant because it provides a standardized, cross-country, and comparable analysis of multidimensional energy poverty in the region. The study of energy poverty is critical for the development and well-being of countries, especially in regions such as South America, where this issue can be affected by geographical, cultural, infrastructure, and/or socio-economic differences. In this study, we measured the magnitude of energy poverty in Argentina, Brazil, Uruguay, and Paraguay. This methodology is based on the analysis of energy poverty through a multidimensional approach, considering three parameters as drivers of energy poverty in the countries: accessibility, availability, and affordability. Through a two-step process, first, we calculate the Weighted Average Energy Poverty Index (WAEPI), based on three proposed scenarios (W1, W2, and W3), and finally, through the Composite Energy Poverty Index (CEPI), we measure the existing gaps, based on the selected indicators, between the countries under study and the benchmark country. Additionally, we decided to focus our analysis on the country that has shown the highest level and gaps on multidimensional energy poverty in the region, as a case study to validate the results obtained through the chosen methodology. The results show that during the period of analysis (2000–2016), Paraguay has been the most energy-poor country among the countries under study, while Argentina has been the least energy-poor country. At the local level, we observed that, Paraguay, despite being one of the largest producers and exporters of clean hydroelectric energy in the region, still presents high levels of consumption of biomass or coal for cooking, while electricity only represents 17% of the total final energy consumption in the country (biomass and fossil fuels account for 83%). These results could lead the design of energy policies, projects, and programs to reduce the multidimensional energy poverty, nationally, also at the common platform: MERCOSUR. Finally, this study includes an analysis of policy implications and alternative solutions to eradicate energy poverty in the region.