Child undernutrition is a major public health problem throughout the world, particularly in developing countries. The main objective of this study was to identify the risk factors for acute undernutrition among under-5 children in Bangladesh. Data were taken from the nationally representative Bangladesh Demographic Health and Survey conducted in 2014. The study sample comprised 7131 under-5 children. Of these, 4.6% were found to be severely wasted (Z-score < −3.0), 11.1% moderately wasted (−3.0≤Z-score < −2.0) and 84.3% adequately nourished (Z-score ≥−2.0). Chi-squared analysis was used to investigate the association between child nutrition status and selected covariates. Multinomial logistic regression was applied to identify the risk factors for acute undernutrition. The selected factors division, place of residence, sex of child, place of delivery, child age, respiratory illness, size at birth, measles vaccination, fever, diarrhoea, maternal BMI, maternal education, paternal occupation, wealth index and household toilet facilities were found to be highly significant (p < 0.05) in the analysis. Multinomial regression analysis revealed that residence in Barisal and Chittagong divisions, a smaller than average size at birth and low maternal BMI (≤18.50 kg/m2) were significant determinants of both moderate and severe acute undernutrition among under-5 children in Bangladesh.