Disparities in birthweight by maternal race/ethnicity are commonly observed. It is unclear to what extent these disparities are correlates of individual socioeconomic factors. In a prospective cohort of 1645 low-risk singleton pregnancies included in the NICHD Fetal Growth Study (2009–2013), neonatal anthropometry was measured by trained personnel using a standard protocol. Socioeconomic characteristics included employment status, marital status, health insurance, annual income, and education. Separate adjusted generalized linear models were fit to both test the effect of race/ethnicity and the interaction of race/ethnicity and socioeconomic characteristics on neonatal anthropometry. Mean infant birthweight, length, head circumference, and abdominal circumference all differed by race/ethnicity (p < 0.001). We observed no statistically significant interactions between race/ethnicity and full-time employment/student status, marital status, insurance, or education in association with birthweight, neonatal exam weight, length, or head or abdominal circumference at examination. The interaction between income and race/ethnicity was significant only for abdominal circumference (p = 0.027), with no other significant interactions for other growth parameters, suggesting that racial/ethnic differences in neonatal anthropometry did not vary by individual socioeconomic factors in low-risk women. Our results do not preclude structural factors, such as lifetime exposure to poverty, as an explanation for racial/ethnic disparities.