The complex interaction between brain and behaviour in language disorder is well established. Yet to date, the imaging literature in the language disorder field has continued to pursue heterogeneous and relatively small clinical cross-sectional samples, with emphasis on cortical structures and volumetric analyses of subcortical brain structures. In our current work, we aimed to go beyond this state of knowledge to focus on the microstructural features of subcortical brain structures (specifically the caudate nucleus) in a large cohort of neonates and study its association with emerging language skills at 24 months. Variations in neonatal brain microstructure could be interpreted as a proxy for in utero brain development. As language development is highly dependent on cognitive function and home literacy environment, we also examined their effect on the caudate–language function relationship utilizing a conditional process model. Our findings suggest that emerging language development at 24 months is influenced by the degree of left lateralization of neonatal caudate microstructure, indexed by diffusion tensor imaging (DTI)-derived fractional anisotropy (FA). FA is an indirect measure of neuronal and dendritic density within grey matter structures. We also found that the caudate–language function relationship is partially mediated by cognitive function. The conditional indirect effect of left caudate FA on language composite score through cognitive function was only statistically significant at low levels of home literacy score (−1 standard deviation [SD]). The authors proposed that this may be related to ‘compensatory’ development of cognitive skills in less favourable home literacy environments.