Preterm-born children are at increased risk of lifelong neurodevelopmental difficulties. Group-wise analyses of magnetic resonance imaging show many differences between preterm- and term-born infants but do not reliably predict neurocognitive prognosis for individual infants. This might be due to the unrecognized heterogeneity of cerebral injury within the preterm group. This study aimed to determine whether atypical brain microstructural development following preterm birth is significantly variable between infants. Using Gaussian process regression, a technique that allows a single-individual inference, we characterized typical variation of brain microstructure using maps of fractional anisotropy and mean diffusivity in a sample of 270 term-born neonates. Then, we compared 82 preterm infants to these normative values to identify brain regions with atypical microstructure and relate observed deviations to degree of prematurity and neurocognition at 18 months. Preterm infants showed strikingly heterogeneous deviations from typical development, with little spatial overlap between infants. Greater and more extensive deviations, captured by a whole brain atypicality index, were associated with more extreme prematurity and predicted poorer cognitive and language abilities at 18 months. Brain microstructural development after preterm birth is highly variable between individual infants. This poorly understood heterogeneity likely relates to both the etiology and prognosis of brain injury.