Overproduction of reactive oxygen species (ROS) and, as a result, uncontrolled oxidative stress (OS) can play a central role in disorders of fetal hemodynamics and subsequent development of adverse perinatal outcomes in newborns with fetal growth restriction (FGR). Given the epigenetic nature of such disorders, the aim of our study was to evaluate the expression of miRNAs associated with OS and endothelial dysfunction (miR-27a-3p, miR-30b-5p, miR-125b-5p, miR-221-3p, miR-451a and miR-574-3p) in umbilical cord blood using real-time quantitative RT-PCR. ΜiRNA expression was evaluated in patients with FGR delivery before (n = 9 pregnant) and after 34 weeks of gestation (n = 13 pregnant), and the control groups corresponding to the main groups by gestational age (13 pregnant women in each group, respectively). A significant increase in miR-451a expression was detected in late-onset FGR and correlations with fetoplacental and cerebral circulation were established (increase of resistance in the umbilical artery (pulsatility index, PI UA (umbilical artery): r = −0.59, p = 0.001) and a decrease in cerebral blood flow (CPR: r = 0.48, p = 0.009)). The change in miR-125b-5p expression in the placenta is associated with reduced Doppler of cerebral hemodynamics (CPR: r = 0.73, p = 0.003; PI MCA (middle cerebral artery): r = 0.79, p = 0.0007), and newborn weight (r = 0.56, p = 0.04) in early-onset FGR. In addition, significant changes in miR-125b-5p and miR-451a expression in umbilical cord blood plasma were found in newborns with neonatal respiratory distress syndrome (NRDS) (in early-onset FGR) and very low birth weight (VLBW) (in late-onset FGR). A number of key signaling pathways have been identified in which the regulation of the studied miRNAs is involved, including angiogenesis, neurotrophin signaling pathway and oxidative stress response. In general, our study showed that changes of the redox homeostasis in the mother-placenta-fetus system in FGR and subsequent perinatal outcomes may be due to differential expression of oxidative stress-associated miRNAs.