In early March 2020, Italy became the epicenter of the Coronavirus Disease 2019 (COVID-19) pandemic in Europe. A different organization of hospital units was required to take care of patients affected by acute respiratory failure caused by COVID-19. This study aimed to evaluate the prevalence of burnout in two sub-intensive care units (SICUs) of the COVID-19 hub center of the Lombardia region in Milan (Italy). All nurses and healthcare assistants working in the SICUs during June 2020 were included in the study. Burnout was assessed via the Maslach Burnout Inventory questionnaire. One hundred and five (84%) SICU staff participated in the study. The prevalence of high burnout for nurses and healthcare assistants was 61.9% for emotional exhaustion, 47.6% for depersonalization and 34.3% for personal accomplishment. Depersonalization was significantly more frequent in younger nurses (p = 0.009). Nurses were 4.5 times more likely to have burnout than healthcare assistants. Burnout was a common condition among healthcare workers operating in SICUs during the pandemic. Urgent actions are needed, especially for nurses, as well as preventive strategies for future pandemic scenarios.