Coronavirus disease 2019 (COVID-19), a condition associated with SARS-CoV-2, typically results in mild infection in infants and children. However, children with risk factors such as chronic lung disease and immunosuppression have higher risk of severe illness from COVID-19. We report a case of a 27-week-gestation extremely premature infant born to a mother with COVID-19 infection. The infant, initially treated for surfactant deficiency, developed worsening hypoxic respiratory failure on the fifth day of life requiring escalating ventilatory support, an elevated level of C-reactive protein, thrombocytopenia, and an elevated level of d-dimer. The infant was positive for SARS-CoV-2 by RT-PCR from Day 1 to Day 42 of his life. The infant responded to a seven-day course of dexamethasone with a gradually decreasing oxygen requirement and could be extubated to non-invasive ventilation by the end of the fifth week after birth. The infant is currently on home oxygen by nasal cannula. Prolonged shedding of the virus may be a unique feature of the disease in premature infants. Extreme prematurity, immature lungs, and an immunocompromised status may predispose these infants to severe respiratory failure and a prolonged clinical course. Instituting appropriate COVID-19 protocols to prevent the spread of the disease in the neonatal intensive care unit (NICU) is of utmost importance. Infection with SARS-CoV-2 may have implications in the management of extremely premature infants in the NICU.