Introduction Child health remains an important public health concern at the global level, with preventable diseases such as diarrheal disease, acute respiratory infection (ARI) and fever posing a large public health burden in low- and middle-income countries including Bangladesh. Improvements in socio-economic conditions have tended to benefit advantaged groups in societies, which has resulted in widespread inequalities in health outcomes. This study examined how socioeconomic inequality is associated with childhood morbidity in Bangladesh, and identified the factors affecting three illnesses: diarrhea, ARI and fever. Materials and methods A total of 43,860 sample observations from the Bangladesh Demographic and Health Survey, spanning a 22-year period (1993-2014), were analysed. Concentration curve and concentration index methods were used to evaluate changes in the degree of household wealth-related inequalities and related trends in childhood morbidity. Regression-based decomposition analyses were used to attribute the inequality disparities to individual determinants for the three selected causes of childhood morbidity. Results The overall magnitude of inequality in relation to childhood morbidity has been declining slowly over the 22-year period. The magnitude of socio-economic inequality as a cause of childhood morbidity varied during the period. Decomposition analyses attributed the inequalities to poor maternal education attainment, inadequate pre-delivery care, adverse chronic undernutrition status and low immunisation coverage. Conclusions High rates of childhood morbidity were observed, although these have declined over time. Socio-economic inequality is strongly associated with childhood morbidity. Socio-economically disadvantaged communities need to be assisted and interventions should emphasise improvements of, and easier access to, health care services. These will be key to improving the health status of children in Bangladesh and should reduce economic inequality through improved health over time.