This study aimed to identify the factors that influence the components of burnout—emotional exhaustion (EE), depersonalization (DP), and personal accomplishment (PA)—among hospital health workers, including doctors and nurses, during the COVID-19 pandemic. We analyzed 200 healthcare workers’ responses to the Employee Health Promotion Survey conducted at a general hospital in Seoul with over 200 hospital beds. The questionnaire included items about COVID-19-related burnout and its influencing factors. We performed three different multiple regression analyses using EE, DP, and PA as the dependent variables. The results show that sex, marital status, workload of treating suspected COVID-19 patients, fear of COVID-19 infection, anxiety, and depression predicted EE. The predictors of DP were job category, consecutive months of work in the current department, satisfaction with work environment, anxiety, and depression. The predictors of PA were the workload of directly interacting with patients, socioeconomic status, and job stress. For EE and DP, burnout was found to be worse in doctors and nurses than in other health workers; moreover, burnout was worse among nurses than among doctors across all three aspects of burnout. The findings can be used to establish tailored policies to address each burnout component.