Background Burnout, a type of long-lasting work-related stress, is highly prevalent among health professionals. It includes dimensions of emotional exhaustion, depersonalization and low professional achievement. Emotional intelligence is the ability to accurately perceive, evaluate, and express emotions, to perceive and/or produce feelings that facilitate thought, to understand emotion and acquire emotional knowledge, and to control emotions in order to promote emotional and intellectual growth. Among the extensive literature on burnout, no studies have measured its prevalence among anesthesiologists in Brazil during the COVID-19 pandemic. Studies on the association between emotional intelligence and burnout are also scarce in this population. The aim of this study was to describe the prevalence of burnout in anesthesiologists at a hospital during the COVID-19 pandemic and to assess its association with emotional intelligence. Methods This cross-sectional study was conducted in a large private hospital in southern Brazil. A non-probabilistic convenience sample of anesthesiologists was selected from a hospital's clinical staff. Via Google Forms, participants responded to an anonymous self-applied self-explanatory questionnaire with sections on sociodemographic data, burnout (Maslach Burnout Inventory), and emotional intelligence (Wong and Law's Emotional Intelligence Scale). Descriptive analysis of the variables was performed and the association between burnout and emotional intelligence was evaluated using the Pearson or Spearman correlation coefficient, depending on data distribution. Results A burnout prevalence of 8.1% was found, as well as a strong negative correlation between total burnout scores and emotional intelligence. Conclusions According to the regression analysis, emotional intelligence can be considered an independent factor associated with this outcome.