What explains the underlying causes of rural–urban differentials in severe acute malnutrition (SAM) among under-five children is poorly exploited, operationalized, studied and understood in low- and middle-income countries (LMIC). We decomposed the rural–urban inequalities in the associated factors of SAM while controlling for individual, household, and neighbourhood factors using datasets from successive demographic and health survey conducted between 2010 and 2018 in 51 LMIC. The data consisted of 532,680 under-five children nested within 55,823 neighbourhoods across the 51 countries. We applied the Blinder–Oaxaca decomposition technique to quantify the contribution of various associated factors to the observed rural–urban disparities in SAM. In all, 69% of the children lived in rural areas, ranging from 16% in Gabon to 81% in Chad. The overall prevalence of SAM among rural children was 4.8% compared with 4.2% among urban children. SAM prevalence in rural areas was highest in Timor-Leste (11.1%) while the highest urban prevalence was in Honduras (8.5%). Nine countries had statistically significant pro-rural (significantly higher odds of SAM in rural areas) inequality while only Tajikistan and Malawi showed statistically significant pro-urban inequality (p < 0.05). Overall, neighbourhood socioeconomic status, wealth index, toilet types and sources of drinking water were the most significant contributors to pro-rural inequalities. Other contributors to the pro-rural inequalities are birth weight, maternal age and maternal education. Pro-urban inequalities were mostly affected by neighbourhood socioeconomic status and wealth index. Having SAM among under-five children was explained by the individual-, household- and neighbourhood-level factors. However, we found variations in the contributions of these factors. The rural–urban dichotomy in the prevalence of SAM was generally significant with higher odds found in the rural areas. Our findings suggest the need for urgent intervention on child nutrition in the rural areas of most LMIC.