Background: The COVID-19 pandemic has strained hospitals and healthcare workers engaged in combating the virus with limited knowledge and resources. Intensive care unit (ICU) nurses are among the healthcare workers most affected by the pandemic and are at risk for developing burnout syndrome. Objective: The present study aims to explore burnout symptoms prevalence among ICU nurses and to identify the individual, organizational, and contextual risk, and protective factors of burnout in ICU nurses during the COVID-19 pandemic. Methods: A scoping review was conducted by searching PubMed, Scopus, and Web of Science. Only papers with empirical data and referred to ICU nurses were included. A total of 350 initial results were yielded, and 40 full texts were screened. Twelve papers constituted the final sample in the analysis. Results: High levels of symptoms of burnout (emotional exhaustion, depersonalization, and reduced personal accomplishment) were registered among ICU nurses during the COVID-19 pandemic. Increased workload, lack of equipment, social stigma, and fear of contagion emerged as key risk factors. Social support from leaders and colleagues, professional recognition, use of personal protective tools, and witnessing patients’ successful recovery emerged as major protective factors. Conclusions: The results may inform the development of timely actions to counter burnout in ICU nurses during this COVID-19 pandemic and in a post-COVID-19 scenario.