(1) Purpose: To analyze the role of job burnout in connection with working hours and subjective well-being (SWB) among hospital administrators in China’s tertiary public hospitals. (2) Methods: A multi-stage, stratified, cluster random sampling method was used to select 443 hospital administrators in six tertiary public hospitals for study. The data were collected and analyzed using the working hours measuring scale, Maslach burnout, and the subjective well-being schedule. Pearson correlation, structural equation model, and bootstrap tests were conducted to examine the association between job burnout, working hours, and SWB. (3) Results: Among the 443 respondents, 330 worked more than 8 h per day on average (76.2%), 81 had the longest continuous working time more than 16 h (18.7%), and 362 worked overtime on weekends (82.2%). The prevalence of job burnout in hospital administrators was 62.8%, among which, 59.8% have mild burnout and 3.00% have severe burnout. In the dimension of emotional exhaustion, depersonalization, and reduced personal achievement, the proportion of people in high burnout was 21.0% (91/433), 15.0% (65/433), and 45.3% (196/433), respectively. Job burnout has a mediating effect between working hours and SWB, which accounted for 95.5% of the total effect. (4) Conclusion: Plagued by long working hours and severe job burnout, the hospital administrators in China’s tertiary public hospitals may have low SWB. Working hours have a negative direct impact on job burnout and SWB, and an indirect impact on SWB through job burnout as a mediator. Targeted strategies should be taken to adjust working hours to promote the physical and mental health of hospital administrators.