Burnout syndrome is considered a chronic response to occupational stressors present in the work environment. Social interactions can constitute one of the stressors at work that generate negative feelings that can trigger a process of contagion of the syndrome among workers in interdependent relationships. The study aimed to analyze whether emotional labor (emotional demands, emotional dissonance) at the level of the leader and subordinate dyad operates together in the manifestation of burnout syndrome. The participants were 244 leader-subordinate dyads who answered a questionnaire with sociodemographic and labor data, the Spanish Burnout Inventory, a subscale of the Questionnaire on the Experience and Assessment of Work, and a subscale of the Frankfurt Emotion Work. Analyses were performed using the actor-partner interdependence model (APIM) through path analysis. The results indicate that the emotional demands of the leaders and the emotional dissonance of the subordinates predict the leader’s burnout syndrome. The Burnout syndrome of subordinates was predicted only by the emotional demands of subordinates. Organizational actions are necessary for the better functioning of this dyad, aiming to mitigate the negative consequences of emotional labor for the worker’s mental health.