Previous studies have shown that sudden changes in the nature of nursing work and their work environment related to the COVID-19 pandemic have affected the professional experience of nurses, and consequently led to an increase in professional burnout in this professional group. Thus, the aim of the study was to measure occupational burnout among nurses working during the COVID-19 pandemic in Poland. A cross-sectional study was conducted with pediatric and surgery female nurses (N = 110, mean age 51 ± 6.92) from the Provincial Specialist Hospital in Włocławek, Poland. The participants completed the Link Burnout Questionnaire (LBQ) and the Socio-Demographic Questionnaire (SDQ). The data were analyzed using Spearman’s rank correlation and Mann–Whitney U test. The study showed that high burnout affected 6.4% of nurses. The level of professional burnout for the subscales of psychophysical exhaustion, relationship deterioration, professional inefficacy and disappointment was 28.2%, 26.4%, 11.8% and 13%, respectively (mean score: 19.85 ± 6.51, 18.03 ± 5.15, 13.74 ± 4.07 and 17.61 ± 5.85, respectively). The results show that surgical nurses were statistically more likely to experience professional burnout. In sum, burnout among nurses has become a serious problem, especially considering the COVID-19 pandemic, which is why it is so important to continue research in this area. Hospital management needs to take urgent action to address the systemic and professional issues that contribute to the suboptimal mental health of nurses.