The health and well-being of school leaders during the COVID-19 pandemic have been largely neglected compared to the health and well-being of students and teachers. This study assessed the magnitude of perceived stress and well-being and the associated factors, including number of working hours, work-related sense of coherence (work-SoC), perceived stress, self-endangering work behaviour, secondary burnout symptoms, and satisfaction with work, among school leaders in Hong Kong, China during the COVID-19 pandemic. This cross-sectional, survey-based study collected demographic data and mental health measurements from 259 eligible school leaders in Hong Kong from April 2021 to February 2022. Pearson’s correlation analyses, multilinear regression models, and independent-samples Student’s t-tests were performed. The findings revealed that school leaders’ perceived stress was negatively correlated with their well-being (r = −0.544, p < 0.01) and work-related SoC (r = −0.327, p < 0.01) but positively correlated with their extensification of work (r = 0.473, p < 0.01), exhaustion related to work situations (r = 0.559, p < 0.01), and psychosomatic complaints (r = 0.439, p < 0.01). In a model that adjusted for gender and age, student leaders with higher subjective well-being scores had a lower level of perceived stress (B = −0.031; 95% confidence interval [CI], −0.59, −0.02; p = 0.034), whereas leaders in schools with a larger student population had a higher level of perceived stress (B = 0.002; 95% CI, 0.000, 0.003; p = 0.030). School leaders with a higher likelihood of performing the self-endangering work behaviour of ‘intensification of work’ had higher perceived stress levels (B = 1.497; 95% CI, 0.717, 2.278; p < 0.001). School leaders with a higher work-related SoC (B = 4.20; 95% CI, 1.290, 7.106; p = 0.005) had a higher level of well-being. School leaders with higher levels of perceived stress (B = −0.734; 95% CI, −1.423, −0.044; p = 0.037), a higher likelihood of performing the self-endangering work behaviour of ‘extensification of work’ (B = −4.846; 95% CI, −8.543, −1.149; p = 0.010), and a higher score for exhaustion related to work (B = −10.449; 95% CI, −13.864, −7.033; p = 0.000) showed lower levels of well-being. The finding of a high incidence of stress among school leadership justifies the need for more societal attention to the well-being of school leaders in Hong Kong. It is important that policies and initiatives are designed to enhance the well-being of school leaders and that they are supported in leading the management of schools and coping with stress in school settings.