The PSNI confirmed officers arrived at an address in Brompton Park in the Ardoyne area of north Belfast after 8.00pm
The emergency services battled to save the baby but the child was pronounced dead at the scene, confirmed police.
A second child, a toddler, who was also injured, was taken to hospital and remains in intensive care.
Detective Chief Inspector Millar from the Police Service of Northern Ireland’s Major Investigation Team said: “Police were called to the house shortly after 8pm last night and discovered the injured baby and another injured child in the house.
“Despite the efforts of the emergency services the baby was sadly pronounced dead at the scene. The other young child was taken to hospital and remains in intensive care.
A 29 year-old woman, who was also in the house, has been arrested on suspicion of murder and attempted murder and remains in custody at this time.
“Our thoughts are with the baby’s family, who are being supported by Family Liaison Officers.”