Safety of healthcare workers in hospitals is a major concern during the COVID-19 pandemic. Being exposed for several working hours per day to infected patients, nurses dealing with COVID-19 face several issues that lead to physical/psychological breakdown. This study focused on burnout and its associated factors in nurses working in an Italian University Hospital during the first wave of COVID-19 pandemic. We designed a web-based cross-sectional study addressed to nurses working at the University Hospital in Foggia, Italy. The online questionnaire was organized in sections aimed at collecting demographic and occupational variables, including the Maslach Burnout Inventory (MBI) and the Oldenburg Burnout Inventory (OBI). Two hundred and ninety-three nurses agreed to participate. According to MBI, we reported moderate/high emotional exhaustion in 76.5%, depersonalization in 50.2%, and personal gratification in 54.6% of participants. COVID-19-related burnout measured by OBI resulted medium/high in 89.1% of participants. Among demographic and occupational factors, a multivariate regression analysis identified emotional support, consideration of leaving job, and workload as predictive of burnout in nurses. In conclusion, this study suggests that the improvement of employer and family support to nurses, as well as reduction of workload and job-related stress, would contribute to reducing burnout in nurses during COVID-19 pandemics.