Maternal diet and nutrient intake are important for fetal growth and development. In this study, we aim to evaluate whether there are associations between maternal diet quality and the offspring’s brain white matter development. Healthy pregnant women’s (N = 44) nutrition intake was assessed by the Healthy Eating Index-2015 (HEI-2015) during the first, second, and third trimesters, respectively. Correlations between MRI diffusion tensor imaging measured fractional anisotropy (FA) of the neonatal brain and the HEI-2015 scores were evaluated using voxel-wise analysis with appropriate multiple comparisons correction and post hoc analysis based on regions of interest. Significant correlations were found between sodium scores at the first trimester of pregnancy and mean neonatal FA values in parietal white matter (R = 0.39, p = 0.01), anterior corona radiata (R = 0.43, p = 0.006), posterior limb of internal capsule (R = 0.53, p < 0.001), external capsule (R = 0.44, p = 0.004), and temporal white matter (R = 0.50, p = 0.001) of the left hemisphere. No other correlations were identified. In conclusion, the relationships between the maternal sodium intake score and the neonatal white matter microstructural development indicate sodium intake patterns better aligned with the Dietary Guidelines for Americans during early pregnancy are associated with greater white matter development in the offspring’s brain.