The purpose of this study was to determine the influence of first-week nutrition intake on neonatal growth in moderate preterm (MP) infants. Data on neonatal morbidity and nutrition intake on day of life 7 (DoL7) were prospectively collected from 735 MP infants (320/7–346/7 weeks gestational age (GA)). Multivariable regression was used to assess the factors associated with extrauterine growth restriction (EUGR) defined as a decrease of more than 1 standard deviation (SD) in the weight z-score during hospitalization. Mean (SD) gestational age and birth weight were 33.2 (0.8) weeks and 2005 (369) g. The mean change in the weight z-score during hospitalization was −0.64 SD. A total of 138 infants (18.8%) had EUGR. Compared to adequate growth infants, EUGR infants received 15% and 35% lower total energy and protein intake respectively (p < 0.001) at DoL7. At DoL7, each increase of 10 kcal/kg/d and 1 g/kg/d of protein was associated with reduced odds of EUGR with an odds ratio of 0.73 (95% CI, 0.66–0.82; p < 0.001) and 0.54 (0.44–0.67; p < 0.001), respectively. Insufficient energy and protein intakes on DoL7 negatively affected neonatal growth of MP infants. Nutritional support should be optimized from birth onwards to improve neonatal weight growth.