Therapeutic hypothermia reduces the incidence of severe motor disability, such as cerebral palsy, following neonatal hypoxic-ischaemic encephalopathy. However, cooled children without cerebral palsy at school-age demonstrate motor deficits and altered white matter connectivity. In this study, we used diffusion-weighted imaging to investigate the relationship between white matter connectivity and motor performance, measured using the Movement Assessment Battery for Children-2, in children aged 6–8 years treated with therapeutic hypothermia for neonatal hypoxic-ischaemic encephalopathy at birth, who did not develop cerebral palsy (cases), and matched typically developing controls. Correlations between total motor scores and diffusion properties in major white matter tracts were assessed in 33 cases and 36 controls. In cases, significant correlations (FDR-corrected P < 0.05) were found in the anterior thalamic radiation bilaterally (left: r = 0.513; right: r = 0.488), the cingulate gyrus part of the left cingulum (r = 0.588), the hippocampal part of the left cingulum (r = 0.541), and the inferior fronto-occipital fasciculus bilaterally (left: r = 0.445; right: r = 0.494). No significant correlations were found in controls. We then constructed structural connectivity networks, for 22 cases and 32 controls, in which nodes represent brain regions and edges were determined by probabilistic tractography and weighted by fractional anisotropy. Analysis of whole-brain network metrics revealed correlations (FDR-corrected P < 0.05), in cases, between total motor scores and average node strength (r = 0.571), local efficiency (r = 0.664), global efficiency (r = 0.677), clustering coefficient (r = 0.608), and characteristic path length (r = -0.652). No significant correlations were found in controls. We then investigated edge-level association with motor function using the network-based statistic. This revealed subnetworks which exhibited group differences in the association between motor outcome and edge weights, for total motor scores (P = 0.0109) as well as for balance (P = 0.0245) and manual dexterity (P = 0.0233) domain scores. All three of these subnetworks comprised numerous frontal lobe regions known to be associated with motor function, including the superior frontal gyrus and middle frontal gyrus. The subnetwork associated with total motor scores was highly left-lateralised. These findings demonstrate an association between impaired motor function and brain organisation in school-age children treated with therapeutic hypothermia for neonatal hypoxic-ischaemic encephalopathy.