We explored the mediating role of burnout on the association between EDW and sleep disturbances. Our study included 18,744 Korean workers. Respondents were grouped into four levels (none, low, moderate, and high) based on their exposure to two EDW factors: handling angry clients (HAC) and hiding emotion (HE). Mediation models were used to estimate odds ratios (OR) at a 95% confidence interval (CI). Compared to those not exposed, low, moderate, and high HAC increased odds of sleep disturbance by 1.52 (95% CI 1.30–1.78), 3.20 (95% CI 2.57–3.98), and 3.28 (95% CI 2.77–3.88) times, respectively. The indirect effect via burnout accounted for 29.9%, 24.1%, and 23.6% of the total effect, respectively, with estimates of 1.13 (95% CI 1.11–1.16), 1.32 (95% CI 1.26–1.39), and 1.32 (95% CI 1.27–1.37). Low, moderate, and high HE increased the odds of sleep disturbance by 1.45 (95% CI 0.93–2.28), 2.38 (95% CI 1.57–3.61), and 3.14 (95% CI 2.08–4.71) times, respectively. The indirect effect via burnout accounted for 10.5%, 29.7%, and 33.1% of the total effect, with estimates of 1.04 (95% CI 0.98–1.10), 1.29 (95% CI 1.22–1.37), and 1.46 (95% CI 1.38–1.55), respectively. Effective policies are required to protect the psychological wellbeing of workers who frequently engage in interpersonal tasks.