The prevalence of childhood overweight/obesity is increasing in Bangladesh, yet there is a scarcity of research on this growing public health issue. Although breastfeeding has been identified as a protective factor against overweight/obesity among young children, the evidence is limited in Bangladesh. This study aimed to investigate the association between breastfeeding status and overweight/obesity among children under three years of age in Bangladesh. Data of 12,497 children were compiled from the most recent nationally representative Multiple Indicator Cluster Survey of Bangladesh (2019). The body mass index (BMI) of the children was measured following the World Health Organisation (WHO) guideline, and breastfeeding status was recorded through maternal response. A multivariable binary logistic regression model was performed to estimate the association between breastfeeding status and overweight/obesity, adjusting for other variables. The prevalence of overweight/obesity was 3.6% (3.3% among breastfed children, and 4.9% among non-breastfed children). The regression analyses revealed that breastfeeding was significantly inversely related to childhood overweight/obesity (adjusted odds ratio: 0.711, 95% confidence interval: 0.512 to 0.987, p-value = 0.042). The present study shows the protective effect of breastfeeding on childhood overweight/obesity. This finding calls for incorporating promotion of breastfeeding as a part of multi-sectoral and multi-factorial approaches in national policy to combat this rising problem in Bangladesh. Future longitudinal studies are also needed to understand the causal pathway and to develop effective and culturally sensitive prevention strategies.