Perinatal asphyxia refers to an acute event of cerebral ischemia and hypoxia during the perinatal period, leading to various degrees of brain injury. The mechanisms involved in perinatal asphyxia include the production of reactive oxygen species (ROS), accumulation of intracellular calcium, lipid peroxidation, excitatory amino acid receptor overactivation, energy failure, and caspase-mediated cell death. Both primary and secondary neuronal damage are caused by the overproduction of ROS following a hypoxic/ischemic event. ROS can react with nearly any type of molecule, including lipids, proteins, polysaccharides, and DNA. Neonates who suffer from perinatal asphyxia are prone to oxidative stress, which is characterized by a disruption in the oxidant/antioxidant balance, favoring oxidants over the intracellular and extracellular antioxidant scavenging mechanisms. Current research has focused on developing treatment strategies that potentially improve the endogenous antioxidant neuroprotective mechanisms or minimize injury resulting from hypoxia/ischemia. In this narrative review, we aim to present evidence regarding the contribution of oxidant/antioxidant balance to the pathogenesis and progression of perinatal asphyxia. Also, we aim to explore the role of potential antioxidant therapies as promising treatment strategies for perinatal asphyxia, especially as an adjunct to therapeutic hypothermia in infants with perinatal asphyxia. The current literature on antioxidant treatments in newborns is limited; however, allopurinol, melatonin, and erythropoietin have shown some positive effects in clinical trials. Inhibitors of nitric oxide synthase, N-acetylcysteine, and docosahexaenoic acid have shown promising neuroprotective effects in preclinical studies. Finally, nanotherapeutics could potentially modulate oxidative stress in hypoxemic/ischemic brain injury by targeted medication delivery. Future research on neuroprotectants and their processes is warranted to develop innovative treatments for hypoxia/ischemia in clinical practice.