Mesenchymal stem cells (MSCs) have generated great interest in the fields of regenerative medicine and immunotherapy because of their unique biological properties. Among MSCs, amniotic fluid stem cells (AFS) have a number of characteristics that make them attractive candidates for tissue engineering and cell replacement strategies, particularly for perinatal medicine. If various neonatal conditions, including birth asphyxia, preterm birth, and congenital abnormalities, which result in long-lasting severe impairments, could be predicted during pregnancy, it would allow collection of small samples of amniotic fluid cells by amniocentesis. In vitro culture of these autologous AFS during pregnancy would make them available for use soon after birth. Hypoxic-ischemic encephalopathy (HIE) and myelomeningocele (MMC) are neonatal conditions that cause permanent neurological disability, for which the treatment options are extremely limited. Experiments using animal models of HIE and MMC and human clinical trials have demonstrated that MSCs, including AFS, have beneficial effects on the central nervous system through paracrine influences, indicating that autologous AFS treatment may be applicable for intractable neurological diseases, including HIE and MMC, during the perinatal period. In this review, we focus on recent research related to the therapeutic potential of AFS for perinatal neurological diseases such as HIE and MMC.