Economic progress in India over the past three decades has not been accompanied by a commensurate improvement in the nutritional status of children, and a disproportionate burden of undernutrition is still focused on socioeconomically disadvantaged populations in the poorest regions. This study examined the nutritional status of children under 3 years of age using data from the fourth round of Indian National Family Health Survey conducted in 2015–2016. Child undernutrition was assessed in a sample of 126,431 under-3 children using the anthropometric indices of stunting, underweight and wasting (‘anthropometric failure’) across 640 districts, 5489 primary sampling units and 35 states/UTs of India. Descriptive statistics were used to examine the regional pattern of childhood undernutrition. Multilevel logistic regression models were fitted to examine the adjusted effect of social group (tribal vs non-tribal) and economic, demographic and contextual factors on the risks of stunting, underweight and wasting accounting for the hierarchical nature of the data. Interaction effects were estimated to model the joint effects of socioeconomic position (household wealth, maternal education, urban/rural residence and geographical region) and social group (tribal vs non-tribal) with the likelihood of anthropometric failure among children. The burden of childhood undernutrition was found to vary starkly across social, economic, demographic and contextual factors. Interaction effects demonstrated that tribal children from economically poorer households, with less-educated mothers, residing in rural areas and living in the Central region of India had elevated odds of anthropometric deprivation than other tribal children. The one-size-fits-all approach to tackling undernutrition in tribal children may not be efficient and could be counterproductive.