In order to control the COVID-19 pandemic, the governments of the world started to implement measures regarding social distance and social contacts, including closures of cities, work and study relocations, and work suspension. The epidemical situation and the lockdown of the economy by governments in various countries caused changes in production, changes in the habits of energy consumers and other energy-related changes. This article analyses the impact of the global pandemic on the energy sector and the relationship with the progress to the sustainability of the energy sector. The systematic literature review was performed in the Web of Science (WoS) database. The research follows recommendations of the SALSA (Search, Appraisal, Synthesis and Analysis) and PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) approaches. A total of 113 relevant articles were selected for the analysis. All selected articles were categorized according to their application and impact areas. The five main impact areas of the COVID-19 pandemic to the sustainability of the energy sector were identified: consumption and energy demand; air pollution; investments in renewable energy; energy poverty; and energy system flexibility. Based on the current research findings and perception of the problem, the main insights for future research in the field are provided.