Brain networks respond to sleep deprivation or restriction with increased sleep depth, which is quantified as slow-wave activity (SWA) in the sleep electroencephalogram (EEG). When adults are sleep deprived, this homeostatic response is most pronounced over prefrontal brain regions. However, it is unknown how children's developing brain networks respond to acute sleep restriction, and whether this response is linked to myelination, an ongoing process in childhood that is critical for brain development and cortical integration. We implemented a bedtime delay protocol in 5- to 12-year-old children to obtain partial sleep restriction (1-night; 50% of their habitual sleep). High-density sleep EEG was assessed during habitual and restricted sleep and brain myelin content was obtained using mcDESPOT magnetic resonance imaging. The effect of sleep restriction was analyzed using statistical non-parametric mapping with supra-threshold cluster analysis. We observed a localized homeostatic SWA response following sleep restriction in a specific parieto-occipital region. The restricted/habitual SWA ratio was negatively associated with myelin water fraction in the optic radiation, a developing fiber bundle. This relationship occurred bilaterally over parieto-temporal areas and was adjacent to, but did not overlap with the parieto-occipital region showing the most pronounced homeostatic SWA response. These results provide evidence for increased sleep need in posterior neural networks in children. Sleep need in parieto-temporal areas is related to myelin content, yet it remains speculative whether age-related myelin growth drives the fading of the posterior homeostatic SWA response during the transition to adulthood. Whether chronic insufficient sleep in the sensitive period of early life alters the anatomical generators of deep sleep slow-waves is an important unanswered question.