Malnutrition impairs cognitive, communication, and motor development, but it is not known how nutrition and health are associated with development in children with moderate acute malnutrition (MAM). We aimed to describe motor and language development of children with MAM and explore its nutrition and health-related correlates. This cross-sectional study used baseline data from a nutritional trial in children with MAM aged 6-23 months in Burkina Faso. Motor and language skills were assessed using the Malawi Development Assessment Tool (MDAT). Linear mixed models were used to explore potential correlates of MDAT including socio-economic status, anthropometry, body composition, whole-blood polyunsaturated fatty acids (PUFA), haemoglobin (Hb), iron status, and morbidity. We also assessed child and caregiver participation during MDAT procedures and their associations with correlates and development. MDAT data were available for 1.608 children. Mean (95% CI) MDAT z-scores were -0.39 (-0.45, -0.34) for gross motor, 0.54 (0.48, 0.59) for fine motor, and -0.91 (-0.96, -0.86) for language skills. Children with higher mid-upper arm circumference, weight-for-height, height-for-age, fat-free mass, n-3 PUFAs, Hb, and iron status had better MDAT z-scores, whereas children with more fat mass index, anaemia, illness, and inflammation had poorer z-scores. In addition, children living in larger households or with an unmarried mother had poorer MDAT z-scores. Associations between morbidity and z-scores were largely explained by children's poorer participation during MDAT assessment. The identified factors associated with child development may inform interventions needed to stimulate development during or after management of MAM.