Influenza is an uncommon illness among premature infants in developed modern neonatal intensive care units (NICUs), but if infants do manifest symptoms of this significant illness, they commonly present with an abrupt onset, with temperature instability and upper respiratory tract involvement and, commonly, clinical features similar to bacterial sepsis. Additionally, frequent manifestations include bronchiolitis and pneumonia. Influenza infection in premature infants is likely a result of reduced levels of passively transferred protective maternal antibodies. Timely supportive therapy, antiviral agents, and isolation of affected infants to prevent spread of infection may be sufficient protective measures in the NICU. We report a case of a 50-day-old very low-birth-weight premature infant with novel A/H1N1 influenza virus (swine flu). There were no obvious epidemiological conditions in the NICU among patients and staff. The unique presenting symptom was apnea, which required respiratory support by nasal intermittent positive pressure ventilation. Due to the current pandemic, neonatologists should be aware of possible infection of neonates with novel A/H1N1 influenza virus.