Caregiver burden among parents of children with neurological and neurodevelopmental conditions remains an underexplored public health concern in low-resource settings. Perceived stigma and social support may influence caregiver burden, but evidence from Nigeria remains limited. This study examined psychosocial and illness-related predictors of caregiver burden among parents of children with neurological and neurodevelopmental conditions in Ibadan, Nigeria. A cross-sectional survey was conducted among 264 parents recruited from clinical and rehabilitative settings in Ibadan. Data were collected using validated measures of caregiver burden, perceived stigma, and social support. Pearson correlation, hierarchical multiple regression, and one-way analysis of variance (ANOVA) were used for data analysis. Caregiver burden was positively associated with total perceived stigma, enacted stigma, internalised stigma, age, and caregiving duration, while social support was negatively associated with burden at the bivariate level. In the hierarchical regression, age, enacted stigma, and internalised stigma significantly predicted caregiver burden, whereas social support and quality of sleep did not significantly improve the final model. Caregiver burden also differed significantly across illness categories, with higher burden observed among caregivers of children with neuromuscular disorders, stroke/CVO, and cerebral palsy. Perceived stigma, particularly enacted and internalised stigma, was an important correlate of caregiver burden in this sample. The findings highlight the need for stigma-reduction strategies, caregiver-focused psychosocial support, and condition-sensitive approaches to care for families managing childhood neurological and neurodevelopmental conditions in Nigeria.