(1) Background: According to the literature, most outcomes of neonates born to mothers infected with SARS-CoV-2 are favorable. This study aimed to assess the clinical characteristics of newborns born to infected women in a tertiary center in Poznan, Poland. (2) Methods: The study comprised 101 newborns delivered by women infected with SARS-CoV-2. The control group consisted of 101 newborns born before the pandemic. Data were collected retrospectively from the medical records. (3) Results: Most newborns of SARS-CoV-2-positive mothers were delivered by cesarean section—83.17% vs. 40.59% in the control group (p < 0.05). The groups did not differ in Apgar scores and the need for resuscitation. Newborns of SARS-CoV-2-positive mothers were more likely to present with respiratory distress and require respiratory support. The most common diagnosis was transient tachypnea of the newborn, not correlated with the mode of delivery. Newborns of the study group were never exclusively breastfed, 0% vs. 64.36% (p < 0.05). None of the patients in the study group was tested positive for the virus. (4) Conclusions: Infants born to SARS-CoV-2-positive mothers seem to be more at risk of moderate respiratory failure than other newborns. Separation of mother–baby dyads results in a dramatic fall in breastfeeding in the short-term post-partum period.