The coronavirus disease 2019 (COVID-19) pandemic is continuously affecting the lives of all people. Understanding the impact of COVID-19 on pregnancy in terms of morbidity, mortality, and perinatal maternal and fetal outcomes is essential to propose strategies for prevention and infection control. Here, we conducted a systematic review to investigate pregnant women infected with COVID-19 in terms of signs and symptoms, type of delivery, comorbidities, maternal and neonatal outcomes, and the possibility of vertical transmission. A search on Embase and PubMed databases was performed on 31 October 2020. Observational studies and case reports on pregnant women infected with COVID-19 were included without language restrictions. The 70 selected studies included a total of 1457 pregnant women diagnosed with COVID-19 in the first, second, and third trimesters of pregnancy. The most common signs and symptoms were fever, cough, and nausea. The most frequent comorbidities were obesity, hypertensive disorders, and gestational diabetes. Among maternal and fetal outcomes, premature birth (n = 64), maternal death (n = 15), intrauterine fetal death or neonatal death (n = 16), cases of intrauterine fetal distress (n = 28), miscarriage (n = 7), decreased fetal movements (n = 19), and severe neonatal asphyxia (n = 5) were the most frequent. Thirty-nine newborns tested positive for SARS-CoV-2. Additionally, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA was detected in the placenta (n = 13) and breast milk (n = 6). This review indicates that COVID-19 during pregnancy can result in maternal, fetal, and neonatal complications. In addition, SARS-CoV-2 viral exposure of neonates during pregnancy and delivery cannot be ruled out. Thus, we highlight the need for long-term follow-up of newborns from mothers diagnosed with COVID-19 to establish the full implications of SARS-CoV-2 infection in these children.