Increasing alcohol consumption by women of childbearing age contributes to more frequent cases of fetal alcohol spectrum disorder. The cause of the syndrome is fetal alcohol exposure, particularly what is referred to as high prenatal alcohol exposure. Low metabolic activity of fetal enzymes shifts the burden of ethanol removal to maternal metabolism. One of the factors influencing the pathogenesis of FASD is the genetic background. It can determine the rate of elimination of ethanol, thus increasing or decreasing the time of fetal exposure to ethanol and also decreasing its concentration. Genetic polymorphisms could potentially play a significant role in these processes. In the present study, we considered three polymorphisms of genes implicated in the synthesis of enzymes involved in ethanol metabolism, i.e., ADH1b (rs1229984), ADH1b/c (rs1789891), and CYP2E1 (rs3813867). The studied group consisted of 303 children and 251 mothers. Both mothers’ and children’s genotypes were considered in our analysis. There were no statistically significant differences between the respective groups of genotypes of the studied polymorphisms. However, the genetic background of FASD is still elusive.