Background The pandemic exacerbated burnout experienced by healthcare personnel, whose mental health had long been a public health concern before COVID-19. This study used the Copenhagen burnout inventory (CBI) tool to assess burnout and identify predictors among Indian healthcare workers managing COVID-19. Methods A cross-sectional study was conducted from June to December 2022, after the third pandemic wave. A web-based, fillable Google form was used to recruit COVID-19 management professionals from multiple Jaipur district hospitals. Healthcare professionals provided socio-demographic, work-related, and CBI scores. Multiple linear regression was used to control for model covariant independent variables. Results We evaluated the responses of a total of 578 participants with a mean age of 36.59 ± 9.1 years. Based on the CBI cut-off score of 50, 68.1% reported burnout. A total of 67.5%, 56.4%, and 48.6% of healthcare workers reported work-related, personal, and patient-related burnout, respectively. High burnout scores were significantly associated with the nursing profession (β = 7.89, 95% CI; 3.66, 12.11, p < 0.0001). The p-value indicates the probability of observing the data if the null hypothesis is true, and the confidence interval shows the range within which we can be 95% confident that the true effect lies. An independent relationship exists between male gender and higher personal-related burnout scores (β = 4.45, 95% CI 1.9–6.9). Conclusion This study identified key indicators that need further emphasis and the need for organizational and individual-level burnout monitoring in healthcare delivery sectors. Health workers continue to experience burnout due to a combination of personal, professional, and patient-related factors. This underscores the need for targeted organizational and individual interventions. The findings also suggest that the CBI tool could identify healthcare worker burnout risk groups.