The discussion on employee burnout (BOT) has existed in academic literature for a long time. While BOT was identified as a personal issue, there is a lack of a system approach solution. In this regard, a milestone was achieved in 2019 when the World Health Organization (WHO) introduced a new definition of BOT, recognising it as an occupational phenomenon, thereby placing a greater responsibility on organisational leadership to manage it. Since then, different leadership models have been proposed by scholars to reduce the effect of BOT in an organisation. Humble leadership (HL), as a people-first approach, has recently gained importance in organisational management literature. Studies have indicated that HL significantly influences different employee outcomes. However, research on the significance of HL to mitigate BOT of employees was scarce—similarly, on the underlying mechanisms of how and why. While HL has the potential to reduce BOT in an organisation, little or no research has studied it. Acknowledging these knowledge gaps, the basic aim of this study is to enrich the existing body of knowledge by proposing HL as an effective organisational management strategy to reduce the effect of BOT in the healthcare sector. The study introduces two mediators, work engagement (WREN) and subjective wellbeing (SUBW), to explain the underlying mechanism between HL and BOT. The conditional indirect role of altruism (ALM) was also tested. The data were obtained from hospital employees by employing a survey method (questionnaire, n = 303). Structural equation model (SEM) was considered for testing the hypothesised model to study the interrelationships between variables. The results confirmed that the manifestation of HL in an organisation reduces BOT significantly, and WREN and SUBW mediate this relationship. The study also demonstrates the buffering effect of ALM in the above-proposed relationships. The empirical findings offer multiple contributions in theory and practice, among which the most important one was to realise the profound importance of HL in reducing the effect of BOT in healthcare management.