Burnout affects the individuals’ health (physical and mental) being a major threat to public health. Moreover, in a world marked by COVID-19, individuals are faced with numerous work, social and economic challenges. However, the influence of COVID-19 on burnout is something that, given the subject’s richness, lacks detailed and clear studies in Portugal. In this study, we aim to investigate the burnout of Portuguese workers during COVID-19, according to their sociodemographic and occupational characteristics. 295 workers participated in this cross-sectional study, answering the Oldenburg Burnout Inventory (OLBI) and a sociodemographic and occupational characteristics questionnaire. Data were analyzed using the t-test, Mann–Whitney, one-way ANOVA, and Kruskal–Wallis tests. The data show statistically significant differences between some sociodemographic and occupational data. Sociodemographic factors influence burnout such as gender, age, geographical area, marital status, number of children, and academic qualifications. Similarly, occupational factors such as working remotely or not during COVID-19, the economic or social organization’s nature, working hours, public or private organization, and salary affect burnout. We discuss these results and propose clues for future research. With this study, we can outline intervention strategies to mitigate burnout and promote well-being and quality of life for individuals at work.