The goal of this narrative review was to summarize the literature findings regarding the occurrence and predictors of burnout syndrome in medical students in the online learning period during the COVID-19 pandemic. This review of identified relevant studies showed that their results were highly heterogeneous, primarily due to the important differences between described studies. Our study found that the burnout syndrome prevalence in medical students in the online learning period during the COVID-19 pandemic ranged, depending on the applied questionnaires, from 16.7 to 59.9%. The most commonly identified risk factors associated with burnout syndrome during online education were stress, low resilience, lack of social support, lower life satisfaction, and higher years of studies that involve clinical training. Further research is necessary to precisely determine the burden of burnout syndrome and its predictors in order to plan and create effective interventions aimed at improving psychological well-being of the future healthcare workforce.