Wasting and underweight reflect poor nutrition, which in children leads to retarded growth. The aim of this study is to determine the factors associated with wasting and underweight among children aged 0–59 months in Nigeria. A sample of 24,529 children aged 0–59 months from the 2013 Nigeria Demographic and Health Survey (NDHS) was used. Multilevel logistic regression analysis that adjusted for cluster and survey weights was used to identify significant factors associated with wasting/severe wasting and underweight/severe underweight. The prevalence of wasting was 18% (95% Confidence Interval (CI): 17.1, 19.7) and severe wasting 9% (95% CI: 7.9, 9.8). The prevalence of underweight was 29% (95% CI: 27.1, 30.5) and severe underweight 12% (95% CI: 10.6, 12.9). Multivariable analysis revealed that the most consistent factors associated with wasting/severe wasting and underweight/severe underweight are: geopolitical zone (North East, North West and North Central), perceived birth size (small and average), sex of child (male), place/mode of delivery (home delivery and non-caesarean) and a contraction of fever in the two weeks prior to the survey. In order to meet the WHO’s global nutrition target for 2025, interventions aimed at improving maternal health and access to health care services for children especially in the northern geopolitical zones of Nigeria are urgently needed.