Background: There is inconclusive evidence regarding congenital, intrapartum, and postnatal maternal-fetal-neonatal SARS-CoV-2 infections during the COVID-19 pandemic. A narrative review was conducted with the aim of guiding clinicians on the management of pregnant women with respect to congenital, intrapartum, and postnatal maternal-fetal-neonatal SARS-CoV-2 infections and breastfeeding during the COVID-19 pandemic. Methods: Searches were conducted in Web of Science, PubMed, Scopus, Dialnet, CUIDEN, Scielo, and Virtual Health Library to identify observational, case series, case reports, and randomized controlled trial studies assessing the transmission of SARS-CoV-2 from mother to baby and/or through breastfeeding during the COVID-19 pandemic. Results: A total of 49 studies was included in this review, comprising 329 pregnant women and 331 neonates (two pregnant women delivered twins). The studies were performed in China (n = 26), USA (n = 7), Italy (n = 3), Iran (n = 2), Switzerland (n = 1), Spain (n = 1), Turkey (n = 1), Australia (n = 1), India (n = 1), Germany (n = 1), France (n = 1), Canada (n = 1), Honduras (n = 1), Brazil (n = 1), and Peru (n = 1). Samples from amniotic fluid, umbilical cord blood, placenta, cervical secretion, and breastmilk were collected and analyzed. A total of 15 placental swabs gave positive results for SARS-CoV-2 ribonucleic acid (RNA) on the fetal side of the placenta. SARS-CoV-2 RNA was found in seven breastmilk samples. One umbilical cord sample was positive for SARS-CoV-2. One amniotic fluid sample tested positive for SARS-CoV-2. Conclusions: This study presents some evidence to support the potential of congenital, intrapartum, and postnatal maternal-fetal-neonatal SARS-CoV-2 infections during the COVID-19 pandemic. Mothers should follow recommendations including wearing a facemask and hand washing before and after breastfeeding.