Abstract Household air pollution (HAP) from solid fuel use (SFU) for cooking is a major public health threat for women and children in low and middle-income countries. This study investigated the associations between HAP and neonatal, infant, and under-five child mortality in Myanmar. The study consisted of 3249 sample of under-five children in the households from the first Myanmar Demographic and Health Survey 2016. Fuel types and levels of exposure to SFU (no, moderate and high) were proxies for HAP. We estimated covariate-adjusted relative risks (aRR) of neonatal, infant, and under-five child mortality with 95% confidence intervals, accounting for the survey design. The prevalence of SFU was 79.0%. The neonatal, infant, and under-five child mortality rates were 26, 45, and 49 per 1000 live births, respectively. The risks of infant (aRR 2.02; 95% CI 1.01–4.05; p-value = 0.048) and under-five mortality (aRR 2.16; 95% CI 1.07–4.36; p-value = 0.031), but not neonatal mortality, were higher among children from households with SFU compared to children from households using clean fuel. Likewise, children highly exposed to HAP had higher risks of mortality than unexposed children. HAP increases the risks of infant and under-five child mortality in Myanmar, which could be reduced by increasing access to clean cookstoves and fuels.