Interest is growing in the research literature in exploring how child nutrition is affected by sociocultural practices, such as polygyny. However, evaluation of the effect of polygyny on child nutrition is hindered by the complexity of the relationship. This paper investigates the effect of polygyny on anthropometric outcomes while recognising that unobservable household characteristics may simultaneously influence both the decision to form a polygynous union and the ability of the household to adequately nourish children. We apply an instrumental variable approach based on the occurrence of same-sex siblings in a woman’s first two births to generate exogenous variation in polygyny. Using data from the 2008 and 2013 Nigeria Demographic and Health Surveys, we find a detrimental effect of polygyny on child undernutrition. Our results show that the effect of polygyny is substantially reduced when we control for household characteristics, suggesting that part of the link between polygyny and child undernutrition is mediated through these channels. Nevertheless, the estimated coefficients of polygyny remain sizeable and strongly statistically significant even after controlling for these characteristics. Polygynous families may have different behavioural childcare practices, and/or the reduced bargaining power of women associated with polygynous families could be associated with higher rates of child undernutrition.