The COVID-19 outbreak has placed extraordinary demands upon healthcare systems worldwide. Italy’s hospitals have been among the most severely overwhelmed, and as a result, Italian healthcare workers’ (HCWs) well-being has been at risk. The aim of this study is to explore the relationships between dimensions of burnout and various psychological features among Italian healthcare workers (HCWs) during the COVID-19 emergency. A group of 267 HCWs from a hospital in the Lazio Region completed self-administered questionnaires online through Google Forms, including the Maslach Burnout Inventory (MBI), Resilience Scale, and Intolerance of Uncertainty Scale Short Form (IU). Cluster analysis highlighted two opposite burnout risk profiles: low burnout and high-risk burnout. The high-risk group had lower resilience and greater difficulties in tolerating the uncertainty than the low-burnout group. A set of general linear models confirmed that both IU subscales, prospective and inhibition, moderated the relationship between resilience and burnout (specifically in the depersonalization dimension). In conclusion, the results showed that individual levels of resilience and one’s ability to tolerate uncertainty have been significant factors in determining the impact of the COVID-19 emergency on HCWs. The use of emotional strategies that allow individuals to stay in a critical situation without the need to control it appears to protect against burnout in these circumstances.