The impact of exposure to lead on child neurodevelopment has been well established. However, sex differences in vulnerability are still not fully explained. We aimed at evaluating the effect of a low-level lead exposure, as measured between 20 to 24 weeks of pregnancy and in cord blood, on developmental scores up to 24 months of age in 402 children from the Polish Mother and Child Cohort (REPRO_PL). Additionally, sex-dependent susceptibility to lead at this very early stage of psychomotor development was assessed. The blood lead levels were analyzed using inductively coupled plasma mass spectrometry (ICP-MS). In order to estimate the children’s neurodevelopment, the Bayley Scales of Infant and Toddler Development was applied. The geometric mean (GM) for blood lead level during 20–24 weeks of pregnancy was 0.99 ± 0.15 µg/dL and, in the cord blood, it was 0.96 ± 0.16 µg/dL. There was no statistically significant impact of lead exposure during prenatal period on the girls’ psychomotor abilities. Among the boys, we observed lower scores for cognitive functions, along with increasing cord blood lead levels (β = −2.07; p = 0.04), whereas the results for the language and motor abilities were not statistically significant (p > 0.05). Our findings show that fetal exposure to very low lead levels might affect early cognitive domain, with boys being more susceptible than girls. Education on health, higher public awareness, as well as intervention programs, along with relevant regulations, are still needed to reduce risks for the vulnerable population subgroups.